System for pathfinding6016485Abstract A system is disclosed for determining a path in a network that decreases the number of disk accesses needed during the pathfinding computation. The network is divided in to a set of tiles. Certain sub-paths are pre-computed. The pre-computed sub-paths are grouped into webs. When finding a path, the system will perform a pathfinding exploration within the tile for the origin and a pathfinding exploration within the tile for the destination. A number of the webs will be used with the two explorations to determine a path from the origin to the destination. Claims We claim: Description BACKGROUND OF THE INVENTION
TABLE 1
______________________________________
Origin Priority Queue
Origin Visited List
Node Key Node Cost Prev
______________________________________
B 3 A 9 O
G 7 B 3 O
A 9 G 7 O
O 0 --
______________________________________
In step 214, the system determines whether a stopping condition has occurred. There are many stopping conditions which are suitable for the present invention, for example, stopping when a node has been the head node on both the origin priority queue and the destination priority queue. Another stopping condition, which is the stopping condition used in this example, is stopping when the cost of traveling from the origin to the head node in the origin priority queue plus the cost of traveling from the head node of the destination priority queue to the destination is greater than or equal to the total cost of the best connection node. A connection node is the node that appears on the destination visited list and the origin visited list. Total cost of a connection node is the cost from the origin to the connection node plus the cost from the connection node to the destination. The best connection node is the connection node with the lowest total cost. In the present case there is no connection nodes so the stopping condition fails and, in step 204, the system picks a queue. As discussed above, the queue selection algorithm in the present example is alternating; therefore, the system picks the destination queue. In step 206, the system determines whether there are any nodes adjacent to the destination D. In the present example there are two adjacent nodes C and F. In step 208, the system looks at node C and determines whether there is a lower known cost. Since there is not, in step 210 the destination priority queue and visited list are edited to add node C and its cost. The method loops back to step 206 which determines that there is another adjacent node, node F. In step 208, the system determines that there is not a lower known cost known for F. In step 210, the destination priority queue and the destination visited list are edited to add node F. In step 206, the system determines there are no more adjacent nodes to node D and node D is removed from the destination priority queue in step 212. Table 2 reflects the state of the destination priority queue and visited list at this point in the method. The column labeled Next lists the next node along the path from the listed node to the destination when traveling along the path utilizing the lowest cost known.
TABLE 2
______________________________________
Dest. Priority Queue
Dest. Visited List
Node Key Node Cost Next
______________________________________
F 4 C 5 D
C 5 D 0 --
F 4 D
______________________________________
Since there are no connection nodes, the stopping condition fails (step 214) and the system picks the origin priority queue (step 204). From Table 1, it can be seen that the head node on the origin priority queue is node B. The adjacent nodes to node B are nodes A and E. In step 208, there is not a lower known cost for node A. Although node A does appear on the visited list with a cost of 9, the cost of traveling from the origin to node A via node B is 6. That is, the cost of traveling from O to B is 3 and the cost of traveling from B to A is 3. Thus, the cost of traveling from O to B to A is 6 which is lower than the cost of traveling from O directly to A. Therefore, in step 210 the visited list and priority queue are edited so that the cost of traveling to node A is 6 and the previous node in the visited list for node A is B. That is, to get to A from O at a cost of 6 you must travel through node B. In step 206, the system determines that there is another adjacent node, E. In step 208, the system determines that there is not a lower known cost for E and the priority queue and visited list are edited to include E. Table 3 reflects the current state of the origin priority queue and the visited list after node B was removed from the priority queue (step 212).
TABLE 3
______________________________________
Origin Priority Queue
Origin Visited List
Node Key Node Cost Prev
______________________________________
E 5 A 6 B
A 6 B 3 O
G 7 E 5 B
G 7 O
O 0 --
______________________________________
At this point, the stopping condition fails because there is no connection node and the system picks the destination queue (step 204). In step 206, the system looks for nodes adjacent to the head node on the destination queue. Since the head node is node F, the adjacent nodes are nodes E and D. The cost of traveling from E to F is 2, thus, the cost traveling from E to F to D is 6. In step 208, the system determines that there is not a lower known cost for traveling from E to D so the visited list and priority queue are updated accordingly. The cost of traveling from D to F to D is eight which is more than the cost of zero associated with Node D in the visited list, so the visited lot and priority queue are not updated. In step 206, the system determines that there is not another adjacent node and F is removed from the priority queue in step 212. Table 4 reflects the state of the destination priority queue and visited list at this point in the method.
TABLE 4
______________________________________
Dest. Priority Queue
Dest. Visited List
Node Key Node Cost Next
______________________________________
C 5 C 5 D
E 6 D 0 --
E 6 F
F 4 D
______________________________________
In step 214, the system determines whether the stopping condition has been met. At this point there is a connection node. Node E is on the visited list for the origin and the visited list for the destination. The total cost for node E is 11. That is, the cost from traveling from the origin to node E is 5 and from node E to the destination is 6. The stopping condition is not met because the cost of traveling from the origin to the head node in the origin priority queue (E) is 5 and the cost of traveling from the head node of the destination priority queue C to the destination is also 5. The sum of the two costs is 10 which is lower than the total cost for the connection node which is 11, therefore the stopping condition fails and the system picks the origin priority queue in step 204. The head node in the origin priority queue is node E, which has two adjacent nodes: C and F. In step 208, the system determines whether a lower cost for traveling from the origin to F is already known. Since F is not on the origin priority queue, there is no known cost and the cost of traveling from the origin to E to F, which is 7, is added to the origin priority queue and the visited list. In step 206, the system determines that there is another adjacent node C. In step 208, th e system deter mines whether there is a known cost for traveling to C from the origin. The cost of traveling from the origin to E to C is 9. Since there is no known lower cost from traveling from the origin to C, C is added to the priority queue and the visited list. At this point there are no more adjacent nodes to node E and node E is removed from the queue (step 212). Table 5 reflects the current state of the origin priority queue at this point in the method.
TABLE 5
______________________________________
Origin Priority Queue
Origin Visited List
Node Key Node Cost Prev
______________________________________
A 6 A 6 B
G 7 B 3 O
F 7 C 9 E
C 9 E 5 B
F 7 E
G 7 O
O 0 --
______________________________________
In Step 214, the system determines that the stopping condition has been met. At this point there are three connection nodes. The total cost of connection node C is 14, the total cost of connection node F is 11 and the total cost of connect ion node E is 11. Since nodes E and F have the lowest total costs of all the connection nodes, nodes E and F are considered the best connection nodes. Various alternatives within the scope of the present invention may utilize other definitions of "best connection node." The cost of traveling from the origin to the head node on the origin priority queue is 6. The cost of traveling from the head node of the destination priority queue to the destination is 5. Therefore, the cost of traveling to and from the head nodes is eleven, which is equal to the total cost of the best cost connection node, which is also eleven. Thus, the stopping condition is met and the system builds the path in step 216. The step of building the path is as follows. A rule selects some connection node. One such rule is to choose the best connection node. The selected connection node K is looked up in the origin visited list and the previous node P.sub.1 on the path from the origin is found. If P.sub.1 is not the origin, then P.sub.1 is looked up in the visited list and the previous node P.sub.2 is found. This continues until the origin is reached. Suppose the origin is reached as node P.sub.L. Similarly, K is looked up in the destination visited list and the next node N.sub.1 is found. If N.sub.1 is not the destination, then N.sub.1 is looked up in the visited list This continues until the destination is reached. Suppose the destination is reached as node N.sub.M. At this point the path from the origin to the destination is known: it is the path from P.sub.L (the origin) to P.sub.L-1, to P.sub.L-2, . . . , to P.sub.2, to P.sub.1, to K, to N.sub.1, . . . , to N.sub.M-1, to N.sub.M (the destination). In the present example, nodes E and F were both the best connection nodes. The system arbitrarily picks node E. Looking at the visited list in Table 5, the best known cost of traveling from the origin to node E involves traveling from node B to node E. Thus, the path being built will travel from B to E. The system then finds node B in the visited list and determines that the best path to node B is directly from the origin O. At this point the path built includes traveling from O to B to E. After the system reaches the origin, the system builds a path from the connection node to the destination. Looking at the visited list in Table 4, the best path from E to the destination involves traveling from E to F. Thus, F is added to the path. The visited list also indicates that the best path from F to D is directly from F to D. Thus, the path built is O-B-E-F-D. FIG. 5 is a flow chart describing a second method for performing a pathfinding exploration. In some respects, the method of FIG. 5 can be viewed as a parallel version of the method of FIG. 4. That is, the general steps taken in FIG. 5 are similar to the steps taken in FIG. 4; however, the method of FIG. 5 can be used to explore for multiple origins (and/or multiple destinations) simultaneously (in parallel). Looking at FIG. 3, for example, suppose a user requests that the system find a path to D from two origins O and B. Rather than perform the steps of FIG. 4 twice, the system can perform the steps of FIG. 5 to simultaneously find paths from O to D and from B to D. In step 240 of FIG. 5, the system initializes. Step 240 is similar to step 202 of FIG. 4. That is, an origin priority queue, an origin visited list, a destination priority queue and a destination visited list can be set up. A difference between the visited lists of FIG. 5 and the visited lists of FIG. 4 is that each node will have a cost and previous column for each origin (or destination). In the example of determining paths from O to D and B to D of FIG. 3, each node in the origin visited list would have two costs and two previous columns. The priority queue of the FIG. 5 process is similar to the priority queue of the FIG. 4 process, except that the priority queue of the FIG. 5 process has an extra column called the Index. As will be explained below, the key for each node on the priority queue is associated with travel between the node in the queue and one of the origins (or one of the destinations). The Index for a node in the priority queue indicates the particular origin (or destination) associated with the key. In one embodiment, the processes of FIG. 4 or FIG. 5 can be performed by exploring from the origin and not from the destination; therefore, an origin priority queue and origin visited list are used but no destination priority queue or destination visited list are used. In another embodiment, the processes of FIG. 4 and FIG. 5 can explore from the destination and not from the origin; therefore, a destination priority queue and a destination visited list are used but no origin priority queue or origin visited list are used. In step 242, the system picks a queue, similar to step 204. If the system is exploring from the origin and not from the destination, then there is no need to pick a queue and step 242 can be skipped. In step 244, the system determines whether there is another adjacent node that has not been considered. The system will look for adjacent nodes to the head node on the priority queue. If there is another adjacent node, the system performs step 246 which includes determining costs to the adjacent node, through the head node, from all of the origins (or all of the destinations). Each of the costs determined in step 246 is a new cost. Each new cost is associated with an origin and an intermediate node. In step 248, the system determines whether a lower or equal cost is already known for any origin/intermediate node pair for which a new costs was determined in step 246. If so, the system loops back to step 244. If not, then the priority queue and visited list are edited in step 250. When editing the visited list, if the node was not on the visited lists, it is added with each new cost. If the node was already on the visited list, then the new costs are added and will replace any existing higher costs, but not replace existing lower costs. If the adjacent node is not on the priority queue, then editing the priority queue includes adding that node to the priority queue with a key equal to the lowest cost of the set of new costs. If the adjacent node is on the priority queue and the lowest cost of the set of new costs is lower than the key, the key is updated to the lowest cost of the set of new costs. If a node's key is updated, the node's corresponding Index is also updated. In step 244, if there are no more adjacent nodes to the head node on the priority queue, then the head node from the appropriate priority queue is removed in step 252 and the system determines whether a stopping condition has been met in step 254. The stopping conditions can be any of the above-described stopping conditions explained with respect to step 214. Alternatively, the stopping condition can be met when there are no more nodes in the priority queue(s). In one embodiment, the stopping condition is met if all the destinations have been reached and the key of the head node of the origin priority queue is greater than the greatest known cost from any origin to any destination along a path that can be built from the visited list. Another embodiment uses the stopping condition described in the previous sentence as a primary stopping condition and also tests for a secondary stopping condition. A suitable secondary stopping condition is met when the priority is empty, with no nodes beyond a distance X from the nearest origin being added to the priority queue during the pathfinding process. One example of a distance X is twice the maximum as the crow flies distance between any origin and destination. If the stopping condition has not been met, the system loops back to step 242 and picks the next queue. If the stopping condition has been met, then the system builds paths in step 256. Since the method is performed for multiple origins or multiple destinations, multiple paths are built. For exemplar purposes, assume that a user only wants to determine two paths in the network of FIG. 3: O to D and B to D. Since there are two origins, both origins are initially placed in the priority queue. Any order will do. Assume that O is the first head node. Table 6 shows the origin priority queue and visited list after step 240. The costs of traveling from origin O to node B and from origin B to node O is initially set at infinity.
TABLE 6
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cost/B Prev/B
______________________________________
O 0 O B Inf. -- 0 --
B 0 B O 0 -- Inf. --
______________________________________
In this example, assume that the system is only exploring from the origin; therefore, there is no need to pick a queue in step 242. In step 244, the system determines that there are three adjacent nodes A, B and G. The system arbitrarily picks node A in step 244 and determines the cost of traveling from the origins through the head node to A. At this point the only path and cost that can be determined are directly from O to A with a cost of 9. There are no paths from B to A, through O, that can be determined at the moment. Since there is no lower cost known, the system edits the visited list and priority queue in step 250 and loops back to step 244 and picks node B. The costs of traveling from O to B is 3 (step 246), there is no lower cost known (step 248), the system edits the visit list and priority queue (step 250), and the system loops back to step 244 to consider node G. The cost of traveling from O to G is 7 (step 246), there is no lower cost known (step 248), the system edits the visit list and priority queue (step 250) and loops back to step 244. At this point, there are no additional adjacent nodes to the head node O, the head node is removed in step 252 and the stopping addition is tested in step 254. Note that B was already in the origin priority queue prior to step 250; however, the key of zero is replaced with a new key of 3. Table 7, below, represents the state of the origin priority queue in origin visit list at this point in the computation.
TABLE 7
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cast/B Prev/B
______________________________________
B 3 O A 9 O Inf. --
G 7 O B 3 O 0 --
A 9 O G 7 O Inf. --
O O -- Inf. --
______________________________________
In this example, the stopping condition is met if all of the destinations have been reached and the head node of the origin priority queue is greater than the known cost from any origin to any destination. At this point in the computation none of the destinations have been reached; therefore, the stopping the condition fails (step 254). The head node on the priority queue is B. Node B has two adjacent nodes A and E. In step 244, the system considers node A. The cost of traveling from B to A is 3 (step 248), so the system adds 3 to the known costs traveling to B from all of the origins. The new cost of traveling from O to A is 6 and the new cost of traveling from B to A is 3. Both these new costs beat the previous old costs of 9 for traveling from O and of infinity from traveling from B, so the visited list and priority queues are updated with the new costs. When the system considers node E, step 246 will be used to determine the cost of traveling from node B to node E as 2. Since there are no previously known costs of traveling to E (step 248), the edited list and priority queue are edited accordingly (step 250). The head node is removed (step 252) and the stopping condition is tested (step 254). At this point the stopping condition fails. Table 8, below, reflects the condition of the origin and priority queue and origin visited list at this point in the computation.
TABLE 8
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cost/B Prev/B
______________________________________
E 2 B A 6 B 3 B
A 3 B B 3 O 0 Inf.
G 7 O E 5 B 2 B
G 7 O Inf. --
O 0 -- Inf. --
______________________________________
Node E is the head note on the priority queue. Node E has two adjacent nodes C and F (step 244). First the system chooses node C. The cost of traveling from node E to node C is 4; therefore, the cost of traveling to node C from O is 9 and traveling to node C from node B is 6 (step 246). Since C is not already on the priority queue or the visit list, there are no known costs (step 248), and the origin priority queue and visit lists are edited accordingly (step 250). The system then loops back to step 244 and considers node F. The cost of traveling from E to F is 2; therefore, the cost of traveling from O to F is 7 and from B to F is 4 (step 246). Since F is not already on the visited list or the priority queue (step 248), both are edited accordingly in step 250. The system loops back to 244 and determines that there are no more adjacent nodes. Head node E is removed in step 252 and the stopping condition is determined to fail in step 254. Table 9, below, reflects the state of the origin priority queue and origin visited list at this point in the computation.
TABLE 9
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cost/B Prev/B
______________________________________
A 3 B A 6 B 3 B
F 4 B B 3 O 0 Inf.
C 6 B C 9 E 6 E
G 7 O E 5 B 2 B
F 7 E 4 E
G 7 O Inf. --
O 0 -- Inf. --
______________________________________
Node A is now at the top of the priority queue. Node A has 3 adjacent nodes C, O and B. The system first chooses node O. The cost of traveling from node A to node O is 9; thus, the path from origin O through the head node back to origin O is 15. The path from B to A to O is 12. In step 248, the system determines that there is not a lower cost known for every single origin. There is a lower cost known for one of the origins. That is, the costs already known for getting to node O from node O is zero. This is lower than the new cost of 15; therefore, the new cost is not added to the origin priority queue or the visited list. The new cost of traveling from node B to node is O is 12 which is lower than the already known cost of infinity. Thus, the new cost of 12 was added to the origin visited list in step 250. The system loops back to step 244 and node B is considered. The cost of traveling from A to B is 3. The cost of traveling from origin O to B, via A, is 12 and the cost of traveling from B to A to B is 6. In step 248, the system determines that it has lower costs already known for each of the origins and, therefore, the system does not edit the visit list or origin priority queue and loops back to step 244. In step 244 the system considers node C. The cost of traveling from node A to node C is 4. The new cost of traveling to node C from node O is 13. The new cost of traveling from node B to node C, via node A, is 7. Since there are lower costs known for each origin (step 248) the system loops back to step 244 and does not edit the origin visited list or priority queue. In step 252, the head node is removed. In step 254 it is determined that the stopping condition fails. Table 10 represents the state of the origin priority queue and origin visited list at this point in the computation.
TABLE 10
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cost/B Prev/B
______________________________________
F 4 B A 6 B 3 B
C 6 B B 3 O 0 --
G 7 O C 9 E 6 E
O 12 B E 5 B 2 B
F 7 E 4 E
G 7 O Inf. --
O 0 -- 12 A
______________________________________
Node F is the head node on the priority queue. Node D is the only node adjacent to node F (step 244). In step 246, the system determines the cost of traveling from node F to node D as being 4. Thus, the cost of traveling from O to D is 11 and from B to D as 8 (step 246). Since D is not in the origin visited list or origin priority queue (step 248), the system edits the visited list and priority queue in step 250 to add D and its costs. In step 244, the system determines that there is no further adjacent nodes. The head node is removed in step 252. The stopping condition is tested in step 254. Table 11 reflects the state of the origin priority queue and origin visited list at this point in the computation.
TABLE 11
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cost/B Prev/B
______________________________________
C 6 B A 6 B 3 B
G 7 O B 3 O 0 --
D 8 B C 9 E 6 E
O 12 B D 11 F 8 F
G 5 B 2 B
F 7 E 4 E
G 7 O Inf. --
O 0 -- 12 A
______________________________________
When checking the stopping condition, the system notes that all destinations (in this case 1) have been reached and there is a path known from each origin to each destination. The system must also test whether the key of the head node of the priority queue is greater than the greatest known cost from any origin to any destination along a path that can be built from the visited list. The known costs from the origins to the destinations are O to D with a cost of 11 and B to D with a cost of 8; thus, the greatest known cost is 11. Since 6 is less than 11, the stopping condition fails. The head node of the priority queue is C. There were 3 nodes adjacent to C: A, E and D. When the system performs steps 244-250 for nodes A, E and D, the system will determine new costs all of which are greater than the costs already known; therefore, the priority queue and visited list will not be edited for any of these 3 adjacent nodes. After the head node C is removed from the priority queue, the stopping condition will fail because the cost for new head node G is 7, which is still lower than 11. Node G is now the head node on the priority queue. Node G has three adjacent nodes: O, H and I. The system first considers node H in step 244. The costs of traveling from G to H is 5. The cost of traveling from O to G to H is 12. Since there is no cost/path in the visited list for traveling to G from B, the system can not determine a path for traveling from node B to node H via node G; therefore, the cost of traveling to nodes G and H from node B is recorded as infinite. Since there are no costs known for traveling to node H (step 248), the visited list and priority queues are edited in step 250 and the system moves back to step 244. The system then considers node I. The costs of traveling from O to G to I is 10 and the system can not compute a cost of traveling from B to G to I (step 246). Since I is not already in the priority queue or visited list, there is no costs already known (step 248), the visited list in priority queues are edited in step 250 and the system loops back to step 244 to consider node O. The cost of traveling from O to G to O is 10 (step 246). There is already a lower cost known for traveling to O from O; therefore, the visited list and priority queue are not edited. In step 244, the system determines that there are no more adjacent nodes and the head node is removed in step 252. Table 12 depicts the state of the priority queue and visited list at this point in the computation.
TABLE 12
______________________________________
Origin Priority
Queue Origin Visited List
Node Key Index Node Cost/O Prev/O
Cost/B Prev/B
______________________________________
D 8 B A 6 B 3 B
I 10 O B 3 O 0 --
O 12 B C 9 E 6 E
H 12 B D 11 F 8 F
E 5 B 2 B
F 7 E 4 E
G 7 O Inf. --
H 12 G Inf. --
I 10 G Inf. --
O 0 -- 12 A
______________________________________
The stopping condition is still not met because the head node has a key of 8 which is not greater than 11, the cost of traveling from E to D. The head node is D, which has two adjacent nodes: C and F. When the system performs steps 244-250 for nodes C and F, the costs found will be higher than the known costs. Therefore, the priority queue and visited list will not be edited. After the system removes head node D from the priority queue in step 252, the stopping condition will be tested in step 254. The new head node on the priority queue is node I. The key for I is 10. Since 10 is less than the cost of the path from E to D (which is 11) the stopping condition fails. Node G is the only node adjacent to node I. The cost of traveling from O to G, via I, is 13. The cost of traveling from B to G, via I, is not known, so the system uses infinity. Since lower (or equal) costs are known for each origin (step 248), the system skips step 250 and loops back to step 244. There are no more adjacent nodes. Node I is removed from the head of the queue (step 252). The new head node is node O, with a cost of 12. The stopping condition is now met because the cost of the head node, which is 12, is greater than the greatest known cost from any origin to any destination, which is 11. The system builds the paths in step 256. The paths built are B-E-F-D and O-B-E-F-D. As the distance between origin node and destination node increases, the number of nodes and links that must be considered in determining a path between the origin and destination can increase greatly. As a result, a system performing a pathfinding calculation on an electronic map may need to perform a tremendous number of computations and may need to perform a large number of disk accesses. This may significantly increase the time required for finding a path between an origin and destination. The present invention is able to decrease the time necessary for pathfinding using the process depicted in FIG. 13. The process of FIG. 13 is employed on network that has been separated into regions called "tiles." A tile can be a region on a graphical map and/or a group of data (or clusters of data) having some geographical relationship. FIG. 6 illustrates one way of dividing the directed graph of FIG. 3 into tiles. A first tile 270 consists of nodes H, G, I and O; a second tile 272 consists of nodes A and B; and a third tile 274 consists of nodes C, D, E, and F. The tiles can be defined by separating geographic regions. Alternatively, tiles can be defined without looking at a visual representation of a graph. For example, a tile can be a set of clusters. An example of clustering technology can be found in U.S. Pat. No. 5,706,503, "Method of Clustering Multi-Dimensional Related Data in a Computer Database," incorporated herein by reference. One method for putting data in clusters includes sorting all the nodes (grouped where there are associated links) by position. The nodes are spatially divided and subdivided to form a k-D tree. The dividing and subdividing continues until the size of the file records needed to represent each subdivision is estimated to be below a nominal target value. The collection of nodes and links in these subdivisions define the clusters. The subdivisions are then ordered with a spatial curve. Sequential cluster records in a file (preferably, but not necessarily) represent spatially contiguous regions in the physical world. Its order should arise naturally. Thus, a network file is created that includes all the clusters ordered according to the spatial curve. Each tile consists of a number of clusters that are contiguous in the network file. The size of a tile should be defined so that it can be read in one disk access. In alternative embodiments, the tile could be bigger and, therefore, may need more than one disk access to be read. For efficiency purposes it is best to pick a tile size to reduce disk accesses. The k-D tree described above is a k-dimensional binary-search tree sometimes called a multidimensional binary tree. One paper of interest in this area is F.P. Preparata and M.I. Shamos, "Computational Geometry: An Introduction," Springer-Verlag (1985). One example of a suitable spatial curve is a Hilbert Curve. In addition to utilizing a network broken up into tiles, the current invention also utilizes a number of webs. A web is defined to be a set of pre-computed paths. The current invention uses four types of webs: an exit-to-entrance web, a vicinity web, a self web and a too-close web. The exit-to-entrance web contains pre-computed paths from the exit nodes of one or more potential origin tiles to the entrance nodes of all or some potential destination tiles. In one embodiment, it may be simpler to have the exit-to-entrance web include only pre-computed paths from exit nodes of one tile to the entrance points of all potential destination tiles. In another embodiment, the exit-to-entrance web includes pre-computed paths from exit nodes for one origin tile to entrance nodes of a set of potential destination files, the set being less than all potential destination tiles. In this alternative, an origin tile may have more than one exit-to-entrance web. In one alternative, the size of the set can be determined such that the exit-to-entrance web can be read with one disk access. An exit node can be thought of as a node that is used after exiting a tile to get to many other places. The set of exit nodes for a particular tile are chosen so that at least one of the exit nodes is on every useful path out of the tile. The entrance node is a node traversed on the way to entering a tile. The set of entrance nodes are chosen such that all useful paths to enter the tile will traverse at least one of the entrance nodes. Determining exit and entrance nodes will be discussed below. The boundary of a tile is defined by a set of exit boundary nodes and entrance boundary nodes. The exit boundary nodes are all of the nodes in a tile that have an outgoing link extending to a node outside of the tile. The entrance boundary nodes are all of the nodes in a tile that have an incoming link extending from a node outside of the tile. A node may be both an exit boundary node and an entrance boundary node. FIG. 7 shows an example of an exit-to-entrance web. Three tiles are depicted in FIG. 7: tile 280, tile 282 and tile 284. Note that, for exemplar purposes, the tiles are shown without any detail. FIG. 7 shows the exit-to-entrance web for tile 280, where the origin is in tile 280 and the destinations will be in tiles 282 or 284. The exit nodes for tile 280 include nodes N, P, R and U. The entrance nodes for tile 282 include nodes J, K and L. The entrance nodes for tile 284 include nodes W, X and Z. All the lines with arrows show possible paths between nodes. Thus, all the paths shown in FIG. 7 are part of paths from the exit nodes of tile 280 to the entrance nodes of tiles 282 or 284. Thus, the paths shown in FIG. 7 comprise the exit-to-entrance web for tile 280. The vicinity web includes pre-computed paths between the boundary nodes of a tile and the exit nodes/entrance nodes of the tile. A tile can have a destination vicinity web for its entrance nodes and an origin vicinity web for its exit nodes. FIG. 8 shows the origin vicinity web for tile 282. Nodes J, K, L, AE and AF represent the exit nodes for tile 282 and nodes AA, AB, AC and AD represent the boundary nodes for tile 282. The lines with arrows show the paths between the boundary nodes and the exit/entrance nodes and, therefore, comprise the vicinity web. The self web includes parts of the pre-computed paths from the exit boundary nodes of a tile to the entrance boundary nodes of the same tile. It is usually best to exclude the parts of the paths that are inside the tile because those parts are already included in the data records that define the tile. An example of an obvious need for a self web is if a tile is cut in half by a river and the only bridge across the river is outside the tile. Thus, travel from an origin to a destination in the same tile may require traveling outside the tile to cross the bridge. FIG. 9 is an example of a self web for tile 282. The paths shown are between the boundary nodes AA, AB, AC and AD. To reduce disk accesses, one embodiment includes combining the data for a tile's self web and vicinity web such that the data for both webs can be read in one disk access. The too-close web includes parts of pre-computed paths between the boundary nodes of one or more origin tiles and the boundary nodes of one or more (or all) destination tiles that are too close to the origin tile for the exit-to-entrance web to be used. For each origin tile-destination tile pair, it is usually best to exclude the parts of the path that are inside the tiles because those parts are included in the data records that define the tiles. An efficient embodiment of the too-close web includes parts of pre-computed paths from the boundary nodes of one origin tile to the boundary nodes of a set of destination tiles that are too close (or within a proximity threshold). The set should include as many too-close destination tiles that allow for the too-close web to be read in one disk access. FIG. 10 shows a too-close web for origin tile 286 and destination tile 288. Tile 286 includes boundary nodes BF, BG, BH, BI and BJ. Tile 288 includes boundary nodes BA, BB, BC, BD and BE. The too-close web includes paths from BF to BA, BG to BA, BG to BB, BG to BC, and BH to BC. FIG. 11 describes one method for determining the exit or entrance nodes for a tile. The method of FIG. 11 could be performed once to find exit nodes and once to find entrance nodes. An alternative method for determining exit/entrance nodes can be found in U.S. patent application Ser. No. 08/756,258, filed Nov. 25, 1996, Richard F. Poppen, "Method For Determining Exits and Entrances For a Region in a Network," now issued as U.S. Pat. No. 5,916,299 incorporated herein by reference. The first step in FIG. 11 is to identify boundary nodes (step 332). As discussed above, boundary nodes include exit boundary nodes and entrance boundary nodes. The exit boundary nodes for a particular tile are all the nodes in the tile that have a link to a node outside the tile. The entrance boundary nodes for a tile are all those nodes inside the tile that have a link from a node outside the tile. Step 332 includes determining whether any of the nodes in a tile under consideration meet either of the conditions of an exit boundary or an entrance boundary node. In addition to identifying a set of exit boundary nodes, a set of exit target nodes are identified for the tile in consideration. Exit target nodes are a set of nodes that cannot be reached from the tile without incurring a sufficient cost C. In one method, the tiles which are partially outside the cost C (i.e. which have some nodes that cannot be reached from the tile without incurring cost C) are noted. Then all the exit boundary nodes of those tiles which have links leading to tiles entirely outside the cost C are exit target nodes. Entrance target nodes are a set of nodes from which the tile cannot be reached without incurring sufficient cost. Such a set may be defined as for the exit target nodes. A sufficient cost is usually, but not always, between 5-50 kilometers. The sufficient cost can be adjusted based on trial and error. Note that the sufficient cost C used to identify the target nodes could be a cost via the network of links or as the crow flies distance. A method for determining the exit target nodes is to run a parallel pathfinding exploration using the method of FIG. 5, using all the exit boundary nodes as origins and only using an origin priority queue (which means exploring from the origins but not exploring from the destinations). As the exploration proceeds, all the tiles through which it passes are noted. When the key for the head node on the priority queue is greater than or equal to C (the sufficient cost used above), the system notes the tile that the head node is in and marks the head node as being beyond C. The exploration continues such that when the system explores from a head node that has been marked as being beyond C, the system, for that head node, only considers travel from the head node to adjacent nodes in the same tile as the head node. Any node in this tile so explored which is a boundary exit node for this tile, and which has a link into a tile which has not been noted as previously explored, is marked as an exit target node. To find the entrance target nodes, the parallel pathfinding exploration of FIG. 5 is performed using the entrance boundary nodes as destinations, only operating on the destination priority queue and following essentially the same procedure as that for finding exit target nodes, except that in the last step we look for boundary entrance nodes instead of boundary exit nodes. In addition to identifying the boundary nodes and target nodes, the system determines paths between the boundary nodes and target nodes in step 336. If the system is trying to find exit nodes, then step 336 is used to find paths between exit boundary nodes and exit target nodes. If the system is trying to find entrance nodes, then paths are determined between entrance target nodes and entrance boundary nodes. The step of determining paths includes utilizing the parallel path exploration of FIG. 5 such that the exit boundary nodes identified in step 332 are the origins, the target nodes identified in step 334 are the destinations and the system only uses an origin priority queue. The parallel pathfinding process will continue until the priority queue is empty. When the origin priority queue is empty, the system builds all possible paths. After determining the paths between the boundary nodes and the target nodes, the system chooses two radii R1 and R2 such that R1<R2 and R2.ltoreq.1/2 C(step 338). Examples of R1 include 1/3C and 1/4C. The value of C is the same value discussed above in regard to finding target nodes. R1 and R2 can be adjusted experimentally in order to optimize and balance having too many exit nodes versus having the exit nodes being too far from the tiles and, thus, less useful. After determining the two radii, the system chooses one pair of nodes. A pair of nodes is defined as a boundary node and a target node such that there is a path between the boundary node and target node. In step 340, the system chooses one of those pairs not already considered. In step 342, the system traverses along the path from the boundary node to the target node and marks all nodes traversed. If any of the nodes traversed and marked in step 342 are high priority nodes (step 344), then the system tests whether any of these high priority nodes are within the two radii (step 350). If any of the high priority nodes are within the two radii (R1 and R2), then the system adds to the score for each of those nodes (step 354). If none of the high priority nodes are within the two radii, then the system finds the best high priority node in step 352, and adds to that node's score in step 354. If step 344 determines that none of the nodes traversed and marked are high priority nodes, then the system loops back to step 340 and chooses a different pair. A high priority node is defined to be a node at which there is a relatively important choice of direction. Perhaps, the high priority node is at an intersection of major roads. Each road in a map, or link in a network, is assigned a true priority. The true priority of a link can, for example, correspond to the typical driving speed for the corresponding road that the link represents. The higher the priority is, the faster the road is. Assuming six different types of roads, the following represents sampled true priorities: alleys-0, residential roads-1, collective roads-2, arterials-3, limited access roads-4 and highways-5. A "shortcut priority" of a link is defined to be the maximum priority Z such that the link is part of the best path from a link of true priority X to a link of true priority Y, and Z is the lower of either X or Y. The "use priority" of a link is defined to be the maximum between the true priority of the link and the shortcut priority of the link. The priority of a node is the maximum use priority for which there are two or more forward links with at least that use priority. In other words, if a node has three forward links (i.e., links leaving the node), with use priorities 1, 1 and 2, respectively, the node is assigned priority 1. If the use priorities of the links from a node are 1, 2, 2, the node would be assigned priority 2. If there is only one forward link, the node has a priority of 0. The process of finding a best node in step 352 includes finding a node that is proportionally the closest to being within the two radii. That is, if a node is inside R1, the system looks at proportional distance D.sub.1 /R1, where D.sub.1 is the distance as the crow flies the node is from R1. If a node is outside R2, the system looks at proportional distance D.sub.2 /R2, where D.sub.2 is the distance of the node from R2. The node with the smallest proportional distance is identified in step 352, unless D.sub.2 is greater than twice R2, in which case the node at D.sub.1 is picked. Before the process of FIG. 11 starts, each node has a score of 0. The first time the process of FIG. 11 is performed, any node whose score is increased in step 354 is increased by a value of 1 each time it is processed in step 354. Since a node may be on many paths, it may have its score increased many times. After a system has increased the scores of the appropriate nodes, the system determines whether there are any more pairs that have not yet been considered (step 360). If there are more pairs, the system loops back to step 340 and a new pair is chosen. If there are no more pairs to consider in step 360, then the system finds the node with the highest score in step 362. In step 364, the node identified in step 362 is admitted to a set of potential exits. In step 366, all paths traveling through the node identified in step 362 are eliminated from a temporary database of paths found in step 336. The system then determines whether any paths remain in that temporary database (step 368). If any paths do remain, the system loops back to step 340 and chooses a pair of boundary/exit nodes to consider. When the system reaches step 368, the list of pairs previously considered is thrown out and initialized such that when the system loops from step 368 to step 340 it is assumed that no pairs have been considered. Thus, steps 340 to 360 are repeated for the entire database (minus paths eliminated). Therefore, steps 340 to 368 are continuously repeated until there are no more paths left in the temporary database. At this point, step 364 has identified a set of many potential exits. After no more paths remain in step 368, the system loops to step 372 and adjusts the weights. The weight is defined to be the amount that a score is increased in step 354. Initially, each score was increased by a weight equal to 1. The paths are re-weighted so that each node on a path has the same weight. The re-weighting is done in such a way that paths which are hard to cover (because there are few acceptable nodes in them) are given higher weight. Each time an exit node and its associated paths are removed, the system assigns a temporary new weight to all the paths. That temporary weight is one divided by the number of paths that were covered by that node. So, if the node covered three paths, each of those three paths is given a temporary weight of 1/3. After all the exits have been found for the current iteration (i.e. all the paths have been removed), the system finds a multiplicative factor for the temporary weights. The multiplicative factor is the reciprocal of the average of all the temporary weights, for all the pairs. In other words, it is the number of pairs divided by the sum of all temporary weights. Next, the system re-weights all the pairs. The system multiplies each temporary weight by the multiplicative factor, and then multiplies that product by the original weight. The system then takes the square root of this product to obtain the new weight for the pair. All the weights are adjusted accordingly. In step 374, the system processes all the nodes another time. Step 374 actually consists of performing another iteration of steps 340 to 372 starting with a full set of paths and all the pairs to be considered, but using the new weights. Therefore, step 374 determines a new set of potential exits. In step 376, the number of nodes in the new set of potential exits is compared against the number of nodes in the immediately previous found set of potential exits. If the recent iteration of step 374 found less exits than the previous set, the system loops back to step 372. If step 374 found more exits, then the process is done and the system uses the previous set of exits for further usage as the exit nodes for the tile (step 380). Entrance nodes are found in a similar manner as exit nodes; however, the system considers paths between entrance target nodes and entrance boundary nodes. The above description notes one particular method for determining entrance nodes and exit nodes. The exact method for determining entrance and exit nodes is not critical to the pathfinding process of FIG. 13. Other suitable methods for determining a reasonable set of exit or entrance nodes may be used without materially effecting the pathfinding computation. Once the exit and entrance nodes are found for each tile, then the webs can be determined for each tile. The exit-to-entrance web for a particular tile is determined by using the parallel pathfinding exploration method of FIG. 5 such that all of the exit nodes for the particular tile are the origins and all the entrance nodes for all of a set of possible destination tiles are the destinations. The exploration for the exit-to-entrance web uses the origin priority queue, does not use the destination priority queue and continues until the priority queues are empty. When an exploration does not use the destination priority queue, then it is only exploring from the origin(s) toward the destination(s). All tiles that are at least further than a proximity threshold from the particular tile in question are considered potential destination tiles and can have their entrance nodes included in the exploration to determine the exit-to-entrance web. The self web is created using the parallel pathfinding exploration of FIG. 5 using the exit boundary nodes as the origins, and entrance boundary nodes as the destinations. The self web is created using an origin priority queue and not using a destination priority queue. The exploration will continue until the origin priority queue is empty or until all the destinations have been reached and the key of the head node of the origin priority queue is greater than the greatest known cost from any origin to any destination along a path that can be built from the visited list. An optional limitation in exploring for the self web is that no path is allowed to be considered that is more than a distance D from the tile. One exemplar D can be twice the diameter of the tile. The too-close web is computed using the parallel pathfinding process of FIG. 5. The exit boundary nodes of the origin tile are used as the origins. The destinations are the entrance boundary nodes of destination tiles that are too close to the origin tile. The processes use the origin priority queue and does not use a destination priority queue. The stopping condition is met when the origin priority queue is empty or if all the destinations have been reached and the key of the head node of the origin priority queue is greater than the greatest known cost from any origin to any destination along a path that can be built from the visited list. An optional limitation placed on the pathfinding exploration is that the system cannot consider paths more than k from either tile, k=2*D, where D is the maximum distance (as the crows flies) between any two points in the origin and destination tiles. FIG. 12 is a flow chart explaining the process of building a vicinity web for a particular tile. The process of FIG. 12 is performed after the process of FIG. 11 and utilizes data determined during the process of FIG. 11. In step 400, the system finds the exit node with the highest score. The score being the final score that was increased in step 354 of FIG. 11. In step 402, the system determines all paths that travel through that exit. The system already knows the paths from the method of FIG. 11. Each of those paths are marked in step 404. Relevant portions of each of the marked paths are added to the vicinity web in step 406. The relevant portions are those sections between the boundary nodes and the exit/entrance nodes. In step 408, the system determines whether there are any exit/entrance nodes that have not been considered. If all such nodes have been considered, then the system is done and the vicinity web is complete in step 410. If there are still exit/entrance nodes that have not been considered, the system loops back to step 400, looks at the set of exit/entrance nodes not yet considered and finds the exit/entrance node with the highest score. FIG. 13 is a flow chart of the pathfinding computation of the present invention. The pathfinding computation is performed, using a processor, on a processor readable representation of a network that has been broken up into tiles and further has been enhanced by including each of the webs discussed above. In step 450, the system receives an indication of an origin. In step 452, the system receives an indication of a destination. Receiving indications of the origin and destination could include a user imputing the origin and destination using a keyboard, a mouse, a light pen, voice recognition technology, etc. If the invention is implemented using software, receiving an indication of the origin and destination could include a call to the appropriate function performing the pathfinding process, passing source and/or destination parameters, or passing one or more pointers to source/destination information. Furthermore, receiving the indication of the source and destination can include reading a permanently hardwired or permanently stored source or destination. After receiving the origin and destination, the system tests whether the origin and destination are in the same tile (step 454). If the origin and destination are in the same tile, the system determines a path from the origin to the destination using the same tile method of step 456. If the origin and destination are not in the same tile, then the system determines, in step 458, whether the origin tile (the tile that the origin resides in) is within a proximity threshold of the destination tile (the tile that the destination resides in). The test whether the tiles are within a proximity threshold of each other can be any one of a number of suitable tests to determine whether it is appropriate to use the too-close web or the exit-to-entrance web. One test is to determine whether the exit nodes of the origin tile are within a constant cost of the entrance nodes of the destination tile. That constant can be determined experimentally. Another test is to determine if any exit node of the origin tile is closer to the destination tile than any entrance node of the destination tile. A third test identifies all of the tiles that are within a proximity threshold of an origin tile as being those tiles that are within an area bounded by the exit target nodes. Alternatively, the tiles that are too close to an origin tile are those tiles that will be explored during the process of finding exit target nodes. If the tiles are within a proximity threshold of each other, then the system performs the process of step 460. If the tiles are not within a proximity threshold of each other, the system performs the process of step 462. After either step 456, step 460 or step 462 are completed, the system loops to step 464 and the path is reported (step 464). The step of reporting the path could include providing a user with turn-by-turn directions on a display, printout or audio output. Additionally, reporting the path could include drawing a map, highlighting a path on a map, creating a file of directions, creating a file of the path, creating a pointer to a file, returning the path as part of a function call, transmitting data from the pathfinding process to a process calling the pathfinding process, etc. FIG. 14 is a flow chart explaining step 456 of FIG. 13 in more detail. The method of FIG. 14 is performed when the source and destination are in the same tile. In step 480, the system reads the data for the tile of the origin and destination. In step 482, the system reads the data for the self web. The terms "self web", "exit-to-entrance web", "vicinity web", and "too-close web" refer to both the data that make up the webs and the actual graphically depicted nodes and links. Further, it is appropriate and equivalent to say that a processor "reads the self web" or "reads the data representing the self web." By the phrase read a tile, read a self web, read data for a tile or read data for a self web, it is meant that the appropriate data is read. In one embodiment, data for the network, including the tiles and webs, is stored on a CD ROM. After the appropriate data is read in steps 480 and 482, the system explores from the origin in step 484 and explores from the destination in step 486. The exploration method used in both steps 484 and 486 is the method depicted in FIG. 4, limited as described below. Steps 484 and 486 can be performed at the same time using separate origin and destination priority queues, or can be performed separately. Exploring from the origin includes using an origin priority queue (and not a destination priority queue) and only considering nodes within the tile and the self web. Exploring from the destination in step 486 includes using a destination priority queue (and not an origin priority queue), and considering nodes in the tile and in the self web. As an alternative, the exploration from the origin could use the self web and the exploration from the destination would not. Both explorations continue until the appropriate priority queue is empty or enough (e.g., 10) connection nodes are found. After both explorations have been completed, the system builds a path (step 488). The path utilizes the best connection node as described above, such that the path minimizes the cost of traveling from the origin to the destination. Note that the steps of FIG. 14 can be performed in a different order than depicted. For example, steps 484 and 486 can performed simultaneously or in reverse order. Steps 480 and 482 can be performed prior to steps 450 and 452, concurrently with steps 450 and 452 or at other appropriate times. FIG. 15 is a flow chart explaining the steps for finding a path using the exit-to-entrance web (step 462 of FIG. 13). In step 500, the system reads the origin tile. In step 502, the system reads the origin self web. In step 504, the system reads the origin vicinity web. Note that the actions of steps 502 and 504 can be combined into a single step. In step 506, the system reads the destination tile. In step 508, the system reads the destination self web. In step 510, the system reads the destination vicinity web. In step 512, the system reads the appropriate exit-to-entrance web for the origin tile and the destination tile. In step 514, the system explores from the origin. In step 516, the system explores from the destination. In step 518, a path is built. Step 514 includes a path exploration using the process of FIG. 4, an origin priority queue (and no destination priority queue), the origin tile, the origin self web and the origin vicinity web. Step 516 includes exploring from the destination using the method of FIG. 4, utilizing the destination priority queue (and no origin priority queue), the destination tile, the destination vicinity web, the destination self web and the exit-to-entrance web for the origin and destination pair. Note that the exploration of steps 514 and 516 continue until their respective priority queues are empty or enough (e.g. 10) connection nodes are found. The path built in step 518 is the path utilizing the best connection nodes as described above. Additionally, the steps of FIG. 15 can be performed in a different order; for example, steps 514 and 516 can be performed in reverse order or simultaneously. The steps of reading the data can also be performed prior to or concurrently with steps 450-454 of FIG. 13. FIG. 16 is a flow chart which explains the steps of determining a path between two tiles that are within the proximity threshold (step 460 of FIG. 13). In step 540, the system reads the origin tile. In step 542, the system reads the self web for the origin tile. In step 544, the system reads destination tile. In step 546, the system reads the self web for the destination tile. In step 548, the system reads too-close web for the destination tile-origin tile pair. In step 550, the system explores from the origin. In step 552, the system explores from the destination. In step 554, a path is built. Exploring from the origin in step 550 includes performing the process of FIG. 4 using an origin priority queue (and not a destination priority queue), the origin tile and the self web for the origin tile. The step of exploring from the destination in step 552 includes performing the process of FIG. 4 using a destination priority queue (and not the origin priority queue), the destination tile, the self web for the destination tile and the too-close web. Both explorations continue until the priority queues are empty or enough (.e.g. 10) connection nodes are found. The path built in step 554 includes traveling through the best connection node, as discussed above. Similar to the processes of FIG. 14 and FIG. 15, the steps of FIG. 16 can be performed in other appropriate orders than as depicted in the drawing. Although the examples used above to describe the present invention were directed to an electronic map of roads, the present invention also applies to any suitable processor readable representation of a network. Suitable networks include a graph of a manufacturing process, intermodal travel plan (e.g., a graph representing travel between points via airplanes, trains, automobiles, busses, etc.), a system for providing medical treatment, etc. For example, if the network represents a manufacturing process, the nodes may represent decision points in the processes (i.e. which station to transport the article of manufacturer or which semiconductor process to use), and the links can represent process time or manufacturing costs. The foregoing detailed description of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The described embodiments were chosen in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.
|
Same subclass | ||||||||||