CA2138092A1 - Method of transmitting communication signals via the shortest route between a pair of nodes in a network - Google Patents
Method of transmitting communication signals via the shortest route between a pair of nodes in a networkInfo
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- CA2138092A1 CA2138092A1 CA 2138092 CA2138092A CA2138092A1 CA 2138092 A1 CA2138092 A1 CA 2138092A1 CA 2138092 CA2138092 CA 2138092 CA 2138092 A CA2138092 A CA 2138092A CA 2138092 A1 CA2138092 A1 CA 2138092A1
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Abstract
A method of transmitting communication signals via the shortest route between a pair of end nodes in a network by executing iterations of the Dijkstra algorithm to recursively determine the shortest routes, from one end node and then from the other end node to other intermediate nodes in the network. The execution of the algorithm is stopped, when one of the nodes, identified as being part of a shortest route proceeding from the one end node, is identified as the other end node.
The execution of the algorithm becomes from one end only when one of the nodes, identified as being part of a shortest route proeeding from the one end node, is identified as one of the nodes closest to the other end node.
The execution of the algorithm becomes from one end only when one of the nodes, identified as being part of a shortest route proeeding from the one end node, is identified as one of the nodes closest to the other end node.
Description
2138~
METHOD OF TRANSMITTING COMMUNICATION SIGNALS VIA
THE SHORTEST ROUTE BETWEEN A PAIR OF NODES IN A
NETWORK
This invention relates to a method of transmitting communication signals via the shortest routes in a network. It is particularly applicable to a network with time varying topology, such as is encountered in telecommunication systems.
A typical telecommunications network has a number of switching nodes interconnected by transmission trunks (bidirectional links) which carry the communication signals. While the physical length of each trunk will generally remain fixed, other operating parameters can vary. For instance, traffic on the network will vary with time and can readily affect operating costs, accessibility and delays times encountered in any one link of the network. It is therefore desirable to be able to dynamically select the shortest route (e.g. least cost, shortest time delay etc.) between any two nodes in the network, to optimize network usage.
One known method utilizes the well known Dijkstra algorithm as described in "Routing In Data Networks", Data Networks, Bertsekas and Gallager, Chapter 5, pp.315-323, 1987. The general approach which follows, is to find the shortest routes in order of increasing route length.
In the network directory, each link (I,J) is characterized by a (direction independent) length LEN(I,J) that can change with time with the following kinds of information being maintained:
1. node labels S(I) indicating distance from the source node;
METHOD OF TRANSMITTING COMMUNICATION SIGNALS VIA
THE SHORTEST ROUTE BETWEEN A PAIR OF NODES IN A
NETWORK
This invention relates to a method of transmitting communication signals via the shortest routes in a network. It is particularly applicable to a network with time varying topology, such as is encountered in telecommunication systems.
A typical telecommunications network has a number of switching nodes interconnected by transmission trunks (bidirectional links) which carry the communication signals. While the physical length of each trunk will generally remain fixed, other operating parameters can vary. For instance, traffic on the network will vary with time and can readily affect operating costs, accessibility and delays times encountered in any one link of the network. It is therefore desirable to be able to dynamically select the shortest route (e.g. least cost, shortest time delay etc.) between any two nodes in the network, to optimize network usage.
One known method utilizes the well known Dijkstra algorithm as described in "Routing In Data Networks", Data Networks, Bertsekas and Gallager, Chapter 5, pp.315-323, 1987. The general approach which follows, is to find the shortest routes in order of increasing route length.
In the network directory, each link (I,J) is characterized by a (direction independent) length LEN(I,J) that can change with time with the following kinds of information being maintained:
1. node labels S(I) indicating distance from the source node;
2. set P of nodes closest to source;
3. set Q of other nodes;
4. a shortest route tree (stored as a table) providing adjacency of nodes in the set P.
To determine the shortest route between a source node and a destination node using Dijkstra:
Step 1 (initialization):
3 5 S(source) = 0 S(I) = LEN(source,I) for nodes I adjacent to the source 21~8~92 S(I) = greater than the total length of any route connecting any two nodes in the network, for all other nodes I
set P contains the source set Q contains all other nodes.
Step 2 (one-step Dijkstra's algorithm):
Find the next closest node I and add it to the set P. Adjust the shortest route tree.
Update label distances S(J) for all nodes J adjacent to node I:
S(J) = min[S(J), S(I)+LEN(I,J)].
Step 3 (stopping criteria):
If P contains all nodes then stop. The algorithm is complete.
Else, go to step 2.
This basic prior art algorithm has been shown to result in the 15 worse case computational complexity, with the complexity being proportional to the power 2 of the number of nodes on the network.
Potentially much can be gained by stopping the calculations when a node I, identified as the closest to the source, turns out to be the destination.
Properties of the Dijkstra algorithm assure that continued execution brings 20 nothing new to the shortest route already determined between the source and destination.
An improved method, described in a paper by T.A.J.
Nicholson, entitled "Finding the shortest route between two points in a network", Computer Journal, No, 9, 1966, pp.275-280, targets selection of a 25 shortest route between two nodes in a network. The procedure is to examine all routes out of the source and into the destination as far as their adjacent connected nodes, and then to extend further the route which has so far covered the least distance. This process is iterative until a route out from the source has a point on it which has already occurred on a route 30 into the destination. The length of this route is as small as the minimum sum of the distances of routes out of the source and routes into the destination, determined thus far.
However, this Nicholson method exhibits some inefficiencies.
One is a bias towards examining all the shortest routes in the 35 neighborhood of one node which could slow down route selection conversion towards the shortest route between the two given nodes. For instance, in a shortest route between two nodes, a part of that route which is in the neighborhood of the destination node might turn out to be significantly longer than a number of shortest routes considered in the neighborhood of the source node, most of which could be leading away from the destination node. Using Nicholson, no consideration is given to the longer route incident to the destination node until all shorter routes have been examined in the neighborhood of the source node.
An example in telecommunications would be when the source node, a switching office, was located in a dense area of the network, closely surrounded by numerous other switching offices, while the destination node, also a switching office, was located in a remote area of the network and was connected by a single very long link to the balance of the network. The Nicholson procedure merely extends the shortest route (i.e.: that closest to the source node) instead of aiming at getting the shortest route as the outcome of the selection.
Also, the stopping condition involves searching for two minima over subsets of nodes examined in the neighborhoods of both end nodes. This is the outcome of the previous inefficiency. Hence, the complexity of this stopping condition verification is proportional to the number of separate shortest routes between both end nodes.
A totally different approach is described in United States Patent 4,987,536 entitled "COMMUNICATION SYSTEM FOR SENDING
AN IDENTICAL ROUTING TREE TO ALL CONNECTED NODES TO
ESTABLISH A SHORTEST ROUTE AND TRANSMITTING MESSAGES
THEREAFTER" issued Jan. 22 1991 to Pierre A. Humblet. Here each reference node receives a routing tree from each adjacent node. Upon receipt the reference node produces a larger tree with itself as the root.
SUMMARY OF THE INVENTION
The inefficiencies of these prior art algorithms have been improved upon in the present invention by a route selection method which:
(1) operates alternately from both end nodes to provide better computational efficiency. This is due to the fact that, on the average, the adjacent subnetwork for each end node is much smaller than the whole ~138~2 network resulting in a much shorter time needed to select the next shortest routes locally, one per end node;
(2) stops operating alternately from both end nodes as soon as a node added to local set of closest nodes is found to have already been included in the set of nodes closest to the other end node then the route selection proceeds from this one end node while the condition for stopping alternate selection remains true; and (3) terminates as early as one end node is identified as the closest node to the other node.
o Thus, in accordance with the present invention there is provided in a communications network having a plurality of nodes, the nodes in the network being interconnected via bidirectional links, a method of transmitting communications signals via the shortest route between a first end node and a second end node selected from a plurality of 15 nodes in a network, the method comprising the steps of: (a) maintaining a directory of the nodes in the network, and the length of each of the bidirectional links; (b) maintaining a record of a first set of nodes, which includes the first end node; (c) maintaining a record of a second set of nodes, which includes the second end node; (d) adding one of the nodes 20 from the directory to a selected one of the sets, the added node being an adjacent one to a node of that one set, and being the next closest node to the end node of that set, to identify the shortest route currently known;
(e) determining: (i) whether the just added node matches the end node of the other set, or (ii) whether the just added node of that one set in the 25 shortest route currently known, match the node of the other set;
(f) selecting: (i) the alternate one of the sets if none of the conditions (e) is true and repeating from step (d) until a match is determined in step (e (i));
and (ii) the same one of the sets if match is determined in step (e(ii)) and repeating from step (d); thereby identifying the shortest route between the 30 end nodes via the matching nodes, over the bidirectional links having the shortest route length; and (g) transmitting communications signals between the end nodes via the shortest route length.
The method of the present invention, which particularly centers around the unique termination criteria, and switching mode of 35 operation from alternate to one-ended, can provide a significant improvement in efficiency over the Dijkstra method where all iterations ~138~92 originate from one end. For instance in a large network if it is assumed that: the number of nodes is proportional to the area covered; and the shortest route to each added node expands radially outward from the end node; then the number of iterations required to find the shortest route
To determine the shortest route between a source node and a destination node using Dijkstra:
Step 1 (initialization):
3 5 S(source) = 0 S(I) = LEN(source,I) for nodes I adjacent to the source 21~8~92 S(I) = greater than the total length of any route connecting any two nodes in the network, for all other nodes I
set P contains the source set Q contains all other nodes.
Step 2 (one-step Dijkstra's algorithm):
Find the next closest node I and add it to the set P. Adjust the shortest route tree.
Update label distances S(J) for all nodes J adjacent to node I:
S(J) = min[S(J), S(I)+LEN(I,J)].
Step 3 (stopping criteria):
If P contains all nodes then stop. The algorithm is complete.
Else, go to step 2.
This basic prior art algorithm has been shown to result in the 15 worse case computational complexity, with the complexity being proportional to the power 2 of the number of nodes on the network.
Potentially much can be gained by stopping the calculations when a node I, identified as the closest to the source, turns out to be the destination.
Properties of the Dijkstra algorithm assure that continued execution brings 20 nothing new to the shortest route already determined between the source and destination.
An improved method, described in a paper by T.A.J.
Nicholson, entitled "Finding the shortest route between two points in a network", Computer Journal, No, 9, 1966, pp.275-280, targets selection of a 25 shortest route between two nodes in a network. The procedure is to examine all routes out of the source and into the destination as far as their adjacent connected nodes, and then to extend further the route which has so far covered the least distance. This process is iterative until a route out from the source has a point on it which has already occurred on a route 30 into the destination. The length of this route is as small as the minimum sum of the distances of routes out of the source and routes into the destination, determined thus far.
However, this Nicholson method exhibits some inefficiencies.
One is a bias towards examining all the shortest routes in the 35 neighborhood of one node which could slow down route selection conversion towards the shortest route between the two given nodes. For instance, in a shortest route between two nodes, a part of that route which is in the neighborhood of the destination node might turn out to be significantly longer than a number of shortest routes considered in the neighborhood of the source node, most of which could be leading away from the destination node. Using Nicholson, no consideration is given to the longer route incident to the destination node until all shorter routes have been examined in the neighborhood of the source node.
An example in telecommunications would be when the source node, a switching office, was located in a dense area of the network, closely surrounded by numerous other switching offices, while the destination node, also a switching office, was located in a remote area of the network and was connected by a single very long link to the balance of the network. The Nicholson procedure merely extends the shortest route (i.e.: that closest to the source node) instead of aiming at getting the shortest route as the outcome of the selection.
Also, the stopping condition involves searching for two minima over subsets of nodes examined in the neighborhoods of both end nodes. This is the outcome of the previous inefficiency. Hence, the complexity of this stopping condition verification is proportional to the number of separate shortest routes between both end nodes.
A totally different approach is described in United States Patent 4,987,536 entitled "COMMUNICATION SYSTEM FOR SENDING
AN IDENTICAL ROUTING TREE TO ALL CONNECTED NODES TO
ESTABLISH A SHORTEST ROUTE AND TRANSMITTING MESSAGES
THEREAFTER" issued Jan. 22 1991 to Pierre A. Humblet. Here each reference node receives a routing tree from each adjacent node. Upon receipt the reference node produces a larger tree with itself as the root.
SUMMARY OF THE INVENTION
The inefficiencies of these prior art algorithms have been improved upon in the present invention by a route selection method which:
(1) operates alternately from both end nodes to provide better computational efficiency. This is due to the fact that, on the average, the adjacent subnetwork for each end node is much smaller than the whole ~138~2 network resulting in a much shorter time needed to select the next shortest routes locally, one per end node;
(2) stops operating alternately from both end nodes as soon as a node added to local set of closest nodes is found to have already been included in the set of nodes closest to the other end node then the route selection proceeds from this one end node while the condition for stopping alternate selection remains true; and (3) terminates as early as one end node is identified as the closest node to the other node.
o Thus, in accordance with the present invention there is provided in a communications network having a plurality of nodes, the nodes in the network being interconnected via bidirectional links, a method of transmitting communications signals via the shortest route between a first end node and a second end node selected from a plurality of 15 nodes in a network, the method comprising the steps of: (a) maintaining a directory of the nodes in the network, and the length of each of the bidirectional links; (b) maintaining a record of a first set of nodes, which includes the first end node; (c) maintaining a record of a second set of nodes, which includes the second end node; (d) adding one of the nodes 20 from the directory to a selected one of the sets, the added node being an adjacent one to a node of that one set, and being the next closest node to the end node of that set, to identify the shortest route currently known;
(e) determining: (i) whether the just added node matches the end node of the other set, or (ii) whether the just added node of that one set in the 25 shortest route currently known, match the node of the other set;
(f) selecting: (i) the alternate one of the sets if none of the conditions (e) is true and repeating from step (d) until a match is determined in step (e (i));
and (ii) the same one of the sets if match is determined in step (e(ii)) and repeating from step (d); thereby identifying the shortest route between the 30 end nodes via the matching nodes, over the bidirectional links having the shortest route length; and (g) transmitting communications signals between the end nodes via the shortest route length.
The method of the present invention, which particularly centers around the unique termination criteria, and switching mode of 35 operation from alternate to one-ended, can provide a significant improvement in efficiency over the Dijkstra method where all iterations ~138~92 originate from one end. For instance in a large network if it is assumed that: the number of nodes is proportional to the area covered; and the shortest route to each added node expands radially outward from the end node; then the number of iterations required to find the shortest route
5 between two nodes applying the Dijkstra algorithm from one end only, could be up to four times the number of iterations required when applying the iterations alternately from both ends, and using the terminating criteria of the present invention.
An example embodiment of the invention will be described with reference to the accompanying drawings in which:
Figure 1 is a schematic representation of a telecommunications network;
Figures 2A to 2F illustrate the progressive selection of the nodes in the network in Figure 1 to determine the shortest route between two end nodes; and Figure 3 is a flow chart of the algorithm used to determine the shortest route.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to Figure 1, there is illustrated a telecommunications network comprising a plurality of switching centers, as represented by nodes 1 to 9 (enclosed in circles), each with its own 25 unique identity. The nodes 1 to 9 are interconnected by communication trunks, represented by bidirectional links, each having a given length (ranging from 1 to 11 in the example) which can vary over time with such operating parameters as the initial and instantaneous operating costs, the queue (time delay) of information packets awaiting transmission or any 30 combination of these and other parameters. When establishing a route between two end nodes, it is desirable to utilize the least cost or shortest route to optimize network utilization. In this example embodiment, the source node 1 and the destination node 9 are the selected end nodes.
Initially, information on the current operating state (length of 35 the bidirectional links and operating state of the nodes) is conveyed over conventional control channels from each of the nodes 1 to 9, to a control 21~8~92 center which typically is at the originating end of the communications link (in the present case the source node 1). The control center at node 1 then performs the following algorithm to determine the shortest route through the network, which can then be used to establish the telecommunications 5 route from the source node 1 to the destination node 9 in a well known manner .
Referring to Figure 3, the algorithm basically comprises the steps of:
1) initializing: i) a directory to include updated information 10 on the length of the links; and ii) two sets of records each including one of the end nodes;
2) selecting one of the sets;
3) executing one step of the Dijkstra algorithm on the selected set;
4) testing to determine whether the shortest route has been found using an unique set of criteria;
5) if so, terminating the execution of the algorithm;
An example embodiment of the invention will be described with reference to the accompanying drawings in which:
Figure 1 is a schematic representation of a telecommunications network;
Figures 2A to 2F illustrate the progressive selection of the nodes in the network in Figure 1 to determine the shortest route between two end nodes; and Figure 3 is a flow chart of the algorithm used to determine the shortest route.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to Figure 1, there is illustrated a telecommunications network comprising a plurality of switching centers, as represented by nodes 1 to 9 (enclosed in circles), each with its own 25 unique identity. The nodes 1 to 9 are interconnected by communication trunks, represented by bidirectional links, each having a given length (ranging from 1 to 11 in the example) which can vary over time with such operating parameters as the initial and instantaneous operating costs, the queue (time delay) of information packets awaiting transmission or any 30 combination of these and other parameters. When establishing a route between two end nodes, it is desirable to utilize the least cost or shortest route to optimize network utilization. In this example embodiment, the source node 1 and the destination node 9 are the selected end nodes.
Initially, information on the current operating state (length of 35 the bidirectional links and operating state of the nodes) is conveyed over conventional control channels from each of the nodes 1 to 9, to a control 21~8~92 center which typically is at the originating end of the communications link (in the present case the source node 1). The control center at node 1 then performs the following algorithm to determine the shortest route through the network, which can then be used to establish the telecommunications 5 route from the source node 1 to the destination node 9 in a well known manner .
Referring to Figure 3, the algorithm basically comprises the steps of:
1) initializing: i) a directory to include updated information 10 on the length of the links; and ii) two sets of records each including one of the end nodes;
2) selecting one of the sets;
3) executing one step of the Dijkstra algorithm on the selected set;
4) testing to determine whether the shortest route has been found using an unique set of criteria;
5) if so, terminating the execution of the algorithm;
6) else selecting the other set and repeating steps 3), 4) and 5).
In the following mathematical description: i) each node is 20 unique and symbolized by capital letter "I"; ii) each link is identified by apair of adjacent nodes (I,J); and iii) each link is characterized by a (direction independent) length LEN(I,J) that can change with time.
The following kinds of information are maintained:
1. node labels Ds(I) and Dd(I) indicating distance of node I
25 from source and from destination, respectively;
2. sets Ps and Pd of nodes closest to source or to destination, respectively;
3. sets Qs and Qd of other nodes, not closest to source or to destination, respectively;
4. shortest route trees TREEs and TREEd (stored as tables) providing adjacency of nodes in the sets Ps and Pd, respectively. (They can be organized as doubly linked lists to speed up search for adjacent nodes in step 6.) 21~9~
Step 1 (initialization):
Ds(source) = O, Dd(destination) = O
Ds(I) = LEN(source,I) for nodes I adjacent to the source Ds(I) = greater than the total length of any route connecting any two nodes in the network, for all other nodes I
Dd(I) = LEN(destination,I) for nodes I adjacent to the destination Dd(I) = greater than the total length of any route connecting any two nodes in the network, for all other nodes I
o set Ps contains the source set Qs contains all other nodes set Pd contains destination set Qd contains all other nodes Go to step 2.
Step 2 (pick a node):
Select an end node to start execution of the computing apparatus. Since the source or destination can be selected equally likely, we shall use a generic term `this end node' and denote it X. Consequently, we shall use Dx to denote distance from X, Px for a set of nodes closest to X, and Qx for a set of other nodes.
Go to step 3.
Step 3 (one-step Dijkstra's al~orithm):
Out of the nodes in the set Qx find the node I closest to this end node X and add it to the set Px. Adjust the shortest route tree in table 2 5 TREEx:
- add a record of node I with distance Dx(I) and a reference (or pointer) to its adjacent node K in a direction towards root node X;
- add a reference (a pointer) to node I, to the record of node K
via which node I is reachable.
Update label distances Dx(J) for all nodes J in set Qx adjacent to node I:
Dx(J) = min[Dx(J), Dx(I)+LEN(I,J)].
Go to step 4.
21~8~92 Step 4 (stoppin~ criterion):
a) If node I is the other end node, then a shortest route has been selected. Go to step 6.
b) Else, if node I is already included in the set P of nodes closest to the other end then continue route selection out of this end. Go to step 3.
Else, go to step 5.
Step 5 (pick the other end node):
Select the other end node to continue execution of the o computing apparatus. If calculations before were done for the source, they will be done now for the destination. If calculations before were done for the destination, they will be done now for the source. Use a generic term `this end node' for the selected end node and denote it X. Consequently, use Dx to denote distance from X, Px for set of nodes closest to X, and Qx for set of other nodes. Go to step 3.
Step 6 (a shortest route is selected):
For stopping criterion (a), the sequence of trunks between node X and the other end node I can be established using node adjacency data in table TREEx.
Repeated iterations of the Dijkstra algorithm using the example embodiment illustrated in Figure 1 are shown in Figures 2A to 2F
in which the objective is to find the shortest route from the source node 1 to the destination node 9. In each of the Figures, the first number in brackets identifies the node, and the second number the total length of the bidirectional links from that node to the end node of that set (either source node 1 or destination node 9).
After initialization of the directory and the sets of records as illustrated in Figure 3, the first iteration of the Dijkstra algorithm is applied to the first set containing the source node 1. Nodes 2, 3, 4 are identified as being: i) not in the first set and ii) adjacent the source node. Of these, node 2 with a route length of 1 is closest to the source node as shown in Figure 2A and is therefore, added to the first set. A test determines that the termination criterion is not met, with the result that the second set (other set) is selected and the algorithm is repeated. This time the nodes, not in 3 5 the second set that are adjacent the end node, are nodes 6, 7, and 8. In thepresent example, node 6 is selected and added to the second set as shown in 21~8~
Figure 2B. Again neither of the termination criteria is met, so the algorithm is again repeated with the first set. This time, node 3 is selected and added to that set, as shown in Figure 2C.
Iterations of the algorithm are repeated as shown in Figures 5 2D, 2E, until the termination criterion is satisfied. This is illustrated in Figure 2F, where it can be seen that node 1, just added to the second set is the source node (the other end node). As a result the algorithm is terminated and the shortest route, comprising nodes 1, 2, 3, 6, 9 with a route length of 10 is selected.
Instead of executing the Dijkstra algorithm consecutively on each of the sets, the algorithm can be executed concurrently on each set using two processors to expedite the determination of the shortest route.
In any case the machine implemented method produces a description of the shortest route between the two selected end nodes, to enable efficient 15 use of the network for the transmission of communications signals and the like.
In the following mathematical description: i) each node is 20 unique and symbolized by capital letter "I"; ii) each link is identified by apair of adjacent nodes (I,J); and iii) each link is characterized by a (direction independent) length LEN(I,J) that can change with time.
The following kinds of information are maintained:
1. node labels Ds(I) and Dd(I) indicating distance of node I
25 from source and from destination, respectively;
2. sets Ps and Pd of nodes closest to source or to destination, respectively;
3. sets Qs and Qd of other nodes, not closest to source or to destination, respectively;
4. shortest route trees TREEs and TREEd (stored as tables) providing adjacency of nodes in the sets Ps and Pd, respectively. (They can be organized as doubly linked lists to speed up search for adjacent nodes in step 6.) 21~9~
Step 1 (initialization):
Ds(source) = O, Dd(destination) = O
Ds(I) = LEN(source,I) for nodes I adjacent to the source Ds(I) = greater than the total length of any route connecting any two nodes in the network, for all other nodes I
Dd(I) = LEN(destination,I) for nodes I adjacent to the destination Dd(I) = greater than the total length of any route connecting any two nodes in the network, for all other nodes I
o set Ps contains the source set Qs contains all other nodes set Pd contains destination set Qd contains all other nodes Go to step 2.
Step 2 (pick a node):
Select an end node to start execution of the computing apparatus. Since the source or destination can be selected equally likely, we shall use a generic term `this end node' and denote it X. Consequently, we shall use Dx to denote distance from X, Px for a set of nodes closest to X, and Qx for a set of other nodes.
Go to step 3.
Step 3 (one-step Dijkstra's al~orithm):
Out of the nodes in the set Qx find the node I closest to this end node X and add it to the set Px. Adjust the shortest route tree in table 2 5 TREEx:
- add a record of node I with distance Dx(I) and a reference (or pointer) to its adjacent node K in a direction towards root node X;
- add a reference (a pointer) to node I, to the record of node K
via which node I is reachable.
Update label distances Dx(J) for all nodes J in set Qx adjacent to node I:
Dx(J) = min[Dx(J), Dx(I)+LEN(I,J)].
Go to step 4.
21~8~92 Step 4 (stoppin~ criterion):
a) If node I is the other end node, then a shortest route has been selected. Go to step 6.
b) Else, if node I is already included in the set P of nodes closest to the other end then continue route selection out of this end. Go to step 3.
Else, go to step 5.
Step 5 (pick the other end node):
Select the other end node to continue execution of the o computing apparatus. If calculations before were done for the source, they will be done now for the destination. If calculations before were done for the destination, they will be done now for the source. Use a generic term `this end node' for the selected end node and denote it X. Consequently, use Dx to denote distance from X, Px for set of nodes closest to X, and Qx for set of other nodes. Go to step 3.
Step 6 (a shortest route is selected):
For stopping criterion (a), the sequence of trunks between node X and the other end node I can be established using node adjacency data in table TREEx.
Repeated iterations of the Dijkstra algorithm using the example embodiment illustrated in Figure 1 are shown in Figures 2A to 2F
in which the objective is to find the shortest route from the source node 1 to the destination node 9. In each of the Figures, the first number in brackets identifies the node, and the second number the total length of the bidirectional links from that node to the end node of that set (either source node 1 or destination node 9).
After initialization of the directory and the sets of records as illustrated in Figure 3, the first iteration of the Dijkstra algorithm is applied to the first set containing the source node 1. Nodes 2, 3, 4 are identified as being: i) not in the first set and ii) adjacent the source node. Of these, node 2 with a route length of 1 is closest to the source node as shown in Figure 2A and is therefore, added to the first set. A test determines that the termination criterion is not met, with the result that the second set (other set) is selected and the algorithm is repeated. This time the nodes, not in 3 5 the second set that are adjacent the end node, are nodes 6, 7, and 8. In thepresent example, node 6 is selected and added to the second set as shown in 21~8~
Figure 2B. Again neither of the termination criteria is met, so the algorithm is again repeated with the first set. This time, node 3 is selected and added to that set, as shown in Figure 2C.
Iterations of the algorithm are repeated as shown in Figures 5 2D, 2E, until the termination criterion is satisfied. This is illustrated in Figure 2F, where it can be seen that node 1, just added to the second set is the source node (the other end node). As a result the algorithm is terminated and the shortest route, comprising nodes 1, 2, 3, 6, 9 with a route length of 10 is selected.
Instead of executing the Dijkstra algorithm consecutively on each of the sets, the algorithm can be executed concurrently on each set using two processors to expedite the determination of the shortest route.
In any case the machine implemented method produces a description of the shortest route between the two selected end nodes, to enable efficient 15 use of the network for the transmission of communications signals and the like.
Claims (4)
1. In a communications network having a plurality of nodes, the nodes in the network being interconnected via bidirectional links, a method of transmitting communications signals via the shortest route between a first end node and a second end node selected from a plurality of nodes in a network, the method comprising the steps of:
(a) maintaining a directory of the nodes in the network, and the length of each of the bidirectional links;
(b) maintaining a record of a first set of nodes, which includes the first end node;
(c) maintaining a record of a second set of nodes, which includes the second end node;
(d) adding one of the nodes from the directory to a selected one of the sets, the added node being an adjacent one to a node of that one set, and being the next closest node to the end node of that set, to identify the shortest route currently known;
(e) determining:
(i) whether the just added node matches the end node of the other set, or (ii) whether the just added node of that one set in the shortest route currently known, match the node of the other set;
(f) selecting:
(i) the alternate one of the sets if none of the conditions (e) is true and repeating from step (d) until a match is determined in step (e (i));
and (ii) the same one of the sets if match is determined in step (e(ii)) and repeating from step (d);
thereby identifying the shortest route between the end nodes via the matching nodes, over the bidirectional links having the shortest route length; and (g) transmitting communications signals between the end nodes via the shortest route length.
(a) maintaining a directory of the nodes in the network, and the length of each of the bidirectional links;
(b) maintaining a record of a first set of nodes, which includes the first end node;
(c) maintaining a record of a second set of nodes, which includes the second end node;
(d) adding one of the nodes from the directory to a selected one of the sets, the added node being an adjacent one to a node of that one set, and being the next closest node to the end node of that set, to identify the shortest route currently known;
(e) determining:
(i) whether the just added node matches the end node of the other set, or (ii) whether the just added node of that one set in the shortest route currently known, match the node of the other set;
(f) selecting:
(i) the alternate one of the sets if none of the conditions (e) is true and repeating from step (d) until a match is determined in step (e (i));
and (ii) the same one of the sets if match is determined in step (e(ii)) and repeating from step (d);
thereby identifying the shortest route between the end nodes via the matching nodes, over the bidirectional links having the shortest route length; and (g) transmitting communications signals between the end nodes via the shortest route length.
2. The method as defined in claim 1 in which step (d) initially includes:
updating each of the records to identify all nodes not in each set, that are adjacent to nodes in each set and the route length from these identified nodes to the end nodes in each set.
updating each of the records to identify all nodes not in each set, that are adjacent to nodes in each set and the route length from these identified nodes to the end nodes in each set.
3. The method as defined in claim 2 in which step (d) initially includes:
updating each of the records to identify all nodes that are not adjacent to a node in the set, and setting the route length from each end node to the nodes that are not adjacent, to a length greater than the total length of any route connecting any two nodes in the network.
updating each of the records to identify all nodes that are not adjacent to a node in the set, and setting the route length from each end node to the nodes that are not adjacent, to a length greater than the total length of any route connecting any two nodes in the network.
4. The method as defined in claim 1 wherein the length of each bidirectional link is the same in the two directions.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US17007393A | 1993-12-16 | 1993-12-16 | |
| US08/170,073 | 1993-12-16 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA2138092A1 true CA2138092A1 (en) | 1995-06-17 |
Family
ID=22618442
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA 2138092 Abandoned CA2138092A1 (en) | 1993-12-16 | 1994-12-14 | Method of transmitting communication signals via the shortest route between a pair of nodes in a network |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA2138092A1 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6266610B1 (en) | 1998-12-31 | 2001-07-24 | Honeywell International Inc. | Multi-dimensional route optimizer |
-
1994
- 1994-12-14 CA CA 2138092 patent/CA2138092A1/en not_active Abandoned
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6266610B1 (en) | 1998-12-31 | 2001-07-24 | Honeywell International Inc. | Multi-dimensional route optimizer |
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