Chong, E.I., S. Maddila, S. Morley, On Finding Single-Source Single-Destination k Shortest Paths, J. Computing and Information, 1995, special issue ICCI'95, pp. 40-47.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....allocated queue space is predefined. The major per formance cftteflon for SAMCRA, namely the running time complexity, will be discussed in paragraph 2.2. Similar to TAMCRA, SAMCRA is based on three fundamental concepts: 1) a non linear measure for the path length, 2) the kshortest path approach [5] and (3) the principle of non dominated paths [12] Before we clarify these three concepts we will first introduce the notations used throughout this paper. A network topology is denoted by G(N, E) where N is the set of nodes and E is the set of links. With a slight abuse of notation we will ....

....path length as (1) is that the subsections of shortest paths in multiple dimensions are not necessarily shortest paths. This suggests to consider in the computation more paths than only the shortest one, leading us naturally to the k shortest path approach. 2. The k shortest path algorithm [5] is essentially Dijkstra s algorithm that does not stop when the destination is reached, but continues until the destination has been reached k times. This concept is applied to the intermediate nodes i on the path from source node s to destination node d, where we keep track of multiple sub paths ....

Chong, E.I., S. Maddila, S. Morley, On Finding Single-Source Single-Destination k Shortest Paths, J. Computing and Information, 1995, special issue ICCI'95, pp. 40-47.

....4 ) In [35] this heuristic algorithm is generalized to more than two constraints with the complexity of O(x 1 : x K 1 n ) or O(x 1 : xK 1 nm) where x 1 ; xK 1 are adjustable integers for each constraint. In [36] the authors used the k shortest path algorithm in [37] with a nonlinear cost function to solve the MCP problem with more than two constraints. The resulting algorithm, called TAMCRA, has a complexity of O(km log(kn) k m) where k is the number of shortest paths. As mentioned above, the performance and overhead of this algorithm depend on k. If k ....

.... m) To improve the performance, the forward direction of H MCOP can also be used with the k shortest path implementation of Dijkstra s al TABLE I RANGES OF LINK WEIGHTS AND THE CORRELATION BETWEEN THEM. Positive correlation No correlation Negative correlation OR OR gorithm presented in [37]. Note that k shortest paths are considered with respect to the minimization of the nonlinear cost function. The complexity of this k shortest path algorithm is m) Hence, the complexity of H MCOP with k shortest paths is O(n log(n) km log(kn) k 1)m) Note that TAMCRA uses the same ....

E. I. Chong, S. R. Sanjeev Rao Maddila, and S. T. Morley, "On finding single-source single-destination k shortest paths," in the Seventh International Conference on Computing and Information (ICCI '95), July 5-8, 1995, pp. 40--47.

.... Routing) to rapidly generate a near optimal delay constrained path in large networks with asymmetric link metrics (delay and cost) This algorithm rst introduces a cost bound according to the network state, then, it employs the k shortest path algorithm proposed by Chong et al. [3] with a new nonlinear weight function of path delay and cost to eciently search for a path subject to both the requested delay constraint and the (introduced) cost constraint. The search space is reduced as paths that now do not satisfy both constraints are pruned o . Our weight function is ....

....10 1 5 5 1 10 c d link cost delay Figure 3: Problem with a non linear function path to the destination through P 1 , with feasible delay and cost of 11, will be missed. De Neve and Van Mieghem solve this problem by taking advantage of the k shortest path algorithm proposed by Chong et al. [3], which can store k shortest paths in increasing weight order at each node. Thus with an appropriate value of k, the algorithm can almost always nd the least weight and feasible path. The non linear (max) weight function in TAMCRA works well so as to nd a path that is far from all the bounds. ....

[Article contains additional citation context not shown here]

E.I. Chong, S. Maddila, and S. Morley. On Finding Single-Source Single-Destination k Shortest Paths. In Proc. International Conference on Computing and Information (ICCI) '95, pages 40-47, Ontario, Canada, July 1995.

....positive integer whose value determines the performance and overhead of the algorithm. To achieve a high probability of finding a feasible path, x needs to be as large as 10n, resulting in computational complexity of O(n 4 ) In [14] Neve and Mieghem used the k shortest paths algorithm in [9] with a nonlinear cost function to solve the MCP problem. The resulting algorithm, called TAMCRA, has a 3 complexity of O(kn log(kn) k 3 Km) where K is the number of constraints. As mentioned above, the performance and overhead of this algorithm depend on k. If it is large, the algorithm ....

E. I. Chong, S. R. Sanjeev Rao Maddila, and S. T. Morley. On finding single-source singledestination k shortest paths. In the Seventh International Conference on Computing and Information (ICCI '95), pages 40--47, July 5-8, 1995. http://styx.trentu.ca/jci/icci/stream95.html. 22

....term above can be omitted. The related problem of finding the k longest paths in a DAG [4] can be transformed to a shortest path problem simply by negating all edge lengths; we can therefore also solve it in the same time bounds. 1. 3 Related Work Many papers study algorithms for k shortest paths [3, 5,7,9,13,14,17,24,31,32,34,35,37 41,43 45, 47, 50, 51, 56 60, 63, 65 69]. Dreyfus [17] and Yen [69] cite several additional papers on the subject going back as far as 1957. One must distinguish several common variations of the problem. In many of the papers cited above, the paths are restricted to be simple, i.e. no vertex can be repeated. This has advantages in some ....

....several common variations of the problem. In many of the papers cited above, the paths are restricted to be simple, i.e. no vertex can be repeated. This has advantages in some applications, but as our results show this restriction seems to make the problem significantly harder. Several papers [3, 13, 17, 24, 41, 42, 58, 59] consider the version of the k shortest paths problem in which repeated vertices are allowed, and it is this version that we also study. Of course, for the DAGs that arise in many of the applications described above including scheduling and dynamic programming, no path can have a repeated vertex ....

E. I. Chong, S. R. Maddila, and S. T. Morley. On finding single-source single-destination k shortest paths. Proc. 7th Int. Conf. Computing and Information, July 1995. http://phoenix.trentu.ca/ jci/papers/icci95/A206/P001.html.

.... Routing) to rapidly generate a near optimal delay constrained path in large networks with asymmetric link metrics (delay and cost) This algorithm rst introduces a cost bound according to the network state, then, it employs the k shortest path algorithm proposed by Chong et al. [4] with a new nonlinear weight function of path delay and cost to e ciently search for a path subject to both the requested delay constraint and the (introduced) cost constraint. The search space is reduced as paths that now do not satisfy both constraints are pruned o . Our weight function is ....

....the actual feasible 1 W (P 1 ) max(10=12; 1=12) 10=12, W (P 2 ) max(5=12; 5=12) 5=12. path to the destination through P 1 , with feasible delay and cost of 11, will be missed. Neve et al.: solve this problem by taking advantage of the k shortest path algorithm proposed by Chong et al. [4], which can store k shortest paths in increasing weight order at each node. Thus with an appropriate value of k, the algorithm can almost always nd the least weight and feasible path. The non linear (max) weight function in TAMCRA works well so as to nd a path that is far from all the bounds. ....

[Article contains additional citation context not shown here]

E.I. Chong, S. Maddila, and S. Morley. On Finding Single-Source Single-Destination k Shortest Paths. In Proc. International Conference on Computing and Information (ICCI) '95, pages 40-47, Ontario, Canada, July 1995.

.... Routing) to rapidly generate a nearoptimal delay constrained path in large networks with asymmetric link metrics (delay and cost) This algorithm first introduces a cost bound according to the network state, then, it employs the k shortest path algorithm proposed by Chong et al. [3] with a new non linear weight function of path delay and cost to efficiently search for a path subject to both the requested delay constraint and the (introduced) cost constraint. Our weight function is designed to give more priority to lower cost paths. This algorithm is very similar to the ....

....node u, path P 2 will be chosen since it has a smaller weight 1 , thus the actual feasible path to the destination through P 1 , with feasible delay and cost of 11, will be missed. Neve et al.: solves this problem by taking advantage of the k shortest path algorithm proposed by Chong et al. [3], which can store k shortest paths in increasing weight order at each node. Thus with an appropriate value of k, the algorithm can almost always find the least weight and feasible path. The non linear (max) weight function in TAMCRA works well so as to find a path that is far from all the bounds. ....

E.I. Chong, S. Maddila, and S. Morley. On Finding Single-Source Single-Destination k Shortest Paths. In Proc. International Conference on Computing and Information (ICCI) '95, pages 40--47, Ontario, Canada, July 1995.

.... Constrained Routing) to rapidly generate a near optimal delay constrained path in large networks with asymmetric link metrics (delay and cost) This algorithm first specifies a cost bound according to the network state, then, it employs the k shortest path algorithm proposed by Chong et al. [3] with a new non linear weight function of path delay and cost to efficiently search for a path subject to both the delay constraint and the cost constraint. Our weight function is designed to give more priority to lower cost paths. This algorithm is very similar to the TAMCRA algorithm proposed by ....

....non linear function For node u, path P 2 will be chosen since it has a smaller weight 1 , thus the actual feasible path P 1 (u; d) with feasible delay and cost of 11, will be missed. Neve et al.: solves this problem by taking advantage of the k shortest path algorithm proposed by Chong et al. [3], which can store k shortest paths in increasing weight order at each node. Thus with an appropriate value of k, the algorithm can almost always find the least weight and feasible path. The non linear (max) weight function in TAMCRA works well so as to find a path that is far from all the bounds. ....

[Article contains additional citation context not shown here]

E.I. Chong, S. Maddila, and S. Morley. On Finding Single-Source Single-Destination k Shortest Paths. In Proc. International Conference on Computing and Information (ICCI) '95, pages 40--47, Ontario, Canada, July 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC