Marta M. B. Pascoal

A new implementation of Yen’s ranking loopless paths algorithm

Abstract.Yen’s algorithm is a classical algorithm for ranking the K shortest loopless paths between a pair of nodes in a network. In this paper an implementation of Yen’s algorithm is presented. Both the original algorithm and this implementation present

DEVIATION ALGORITHMS FOR RANKING SHORTEST PATHS

{\cal O}(Kn(m + n\log n))

Internet packet routing: Application of a K-quickest path algorithm

computational complexity order when considering a worst-case analysis. However, computational experiments are reported, which allow to conclude that in practice this new implementation outperforms two other, Perko’s implementation and a straightforward one.

An algorithm for ranking quickest simple paths

The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K>1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction in considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition – for example, to be loopless. In this paper new algorithms are proposed for the uncontrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths.

Minimum cost path problems with relays

This paper describes a study on the application of an algorithm to rank the K-quickest paths to the routing of data packets in Internet networks. For this purpose an experimental framework was developed by considering two types of random generated networks. To simulate values of the IP packet sizes, a truncated Pareto distribution was defined, having in mind to reflect a key feature of Internet traffic, namely its self-similar stochastic nature. Results concerning the average CPU times of the algorithm for the different sets of experiments will be presented and discussed.

A bicriterion approach for routing problems in multimedia networks

In this paper, an algorithm for ranking loopless paths in undirected networks, according to the transmission time, is presented. It is shown that the worst-case computational time complexity of the algorithm presented is O(Kr(m+n logn)), which is also the best-known complexity to solve this problem. The worst-case memory complexity is O(Kn), which improves the existing algorithms. Finally, comparative computational results, with other algorithms for the same problem, are reported.

A comprehensive survey on the quickest path problem

The minimum cost path problem with relays (MCPPR) consists of finding a minimum cost path from a source to a destination, along which relay nodes are located at a certain cost, subject to a weight constraint. This paper first models the MCPPR as a particular bicriteria path problem involving an aggregated function of the path and relay costs, as well as a weight function. A variant of this problem which takes into account all three functions separately is then considered. Formulating the MCPPR as a part of a bicriteria path problem allows the development of labeling algorithms in which the bound on the weight of paths controls the number of node labels. The algorithm for this constrained single objective function version of the problem has a time complexity of O(Wm+Wnlog(max{W,n})), where n is the number of nodes, m is the number of arcs and W is the weight upper bound. Computational results on random instances with up to 10000 nodes and 100000 arcs, are reported.

Multicriteria path and tree problems: discussion on exact algorithms and applications

Routing problems in communication networks supporting multiple services, namely, multimedia applications, involve the selection of paths satisfying multiple constraints (of a technical nature) and seeking simultaneously to “optimize” the associated metrics. Although traditional models in this area are single-objective, in many situations, it is important to consider different, eventually conflicting, objectives. In this paper, we consider a bicriterion model dedicated to calculating nondominated paths for specific traffic flows (associated with video services) in multiservice high-speed networks. The mathematical formulation of the problem and the bicriterion algorithmic approach developed for its resolution are presented together with computational tests regarding an application to video-traffic routing in a high-speed network. The algorithmic approach is an adaptation of recent work by Ernesto Martins and his collaborators, namely, the MPS algorithm.

A note on a new variant of Murty’s ranking assignments algorithm

This work is a survey on a special minsum-maxmin bicriteria problem, known as the quickest path problem, that can model the transmission of data between two nodes of a network. Moreover, the authors review the problems of ranking the K quickest paths, and the K quickest loopless paths, and compare them in terms of the worst-case complexity order. The classification presented led to the proposal of a new variant of a known K quickest loopless paths algorithm. Finally, applications of quickest path algorithms are mentioned, as well as some comparative empirical results.

On the bicriterion - minimal cost/minimal label - spanning tree problem

Multicriteria/multiobjective path and tree models are useful in many applications. Particularly, in Internet routing problems they seem to lead to promising approaches. In the first part of this paper, we classify and present the main exact approaches dealing with several multicriteria path problems putting in evidence the shortest path problem. In the second part, we review exact algorithms dedicated to some multicriteria tree problems, namely the minimum spanning tree and the minimum cost/minimum label spanning tree problems. Finally, the application of these models is exemplified.