Conference Paper

# Note on the problem of partially link disjoint paths

RMIT Univ., Melbourne, Vic., Australia

DOI: 10.1109/ICICS.2003.1292754 Conference: Information, Communications and Signal Processing, 2003 and the Fourth Pacific Rim Conference on Multimedia. Proceedings of the 2003 Joint Conference of the Fourth International Conference on, Volume: 3 Source: IEEE Xplore

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**ABSTRACT:**Efficient management of networks requires that the shortest route from one point (node) to another is known; this is termed the shortest path. It is often necessary to be able to determine alternative routes through the network, in case any part of the shortest path is damaged or busy. The k-shortest paths represent an ordered list of the alternative routes available. Four algorithms were selected for more detailed study from over seventy papers written on this subject since the 1950's. These four were implemented in the `C' programming language and, on the basis of the results, an assessment was made of their relative performance. 1 The Background The shortest path through a network is the least cost route from a given node to another given node, and this path will usually be the preferred route between those two nodes. When the shortest path between two nodes is not available for some reason, it is necessary to determine the second shortest path. If this too is not available, a thir...12/1997; - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the problem of offering a reliable service in a PNNI network, such that service is almost uninterrupted even if one of the links or nodes in its path goes down. This is done through the provision of alternative paths for each VC that requires this reliable service at the time of call setup. The same approach is also applicable to VP protection switching for establishing alternative soft VPs. We also assume that topological constraints on the network may make it impossible to setup completely disjoint alternative paths, so the alternative paths may be required to be partially disjoint from the primary path. If that is so, the network elements which are common to the primary and alternative paths must be extremely reliable. We formulate this problem as an integer programming problem and show that it can be cast as the well known transportation problem. We compare the performance of the solution of the transportation problem to that of a heuristic based on sequential determination of the alternative paths. The heuristic algorithm delivers good sub-optimal results with lower computational complexity than the optimal transportation algorithm, so it can be used in real-time scenario. For off-line calculations of partially disjoint VPs, the computational complexity of the transportation algorithm is suitable for PNNI networksGlobal Telecommunications Conference, 1998. GLOBECOM 98. The Bridge to Global Integration. IEEE; 02/1998 - [Show abstract] [Hide abstract]

**ABSTRACT:**Let G be a directed graph containing n vertices, one of which is a distinguished source s, and m edges, each with a non-negative cost. We consider the problem of finding, for each possible sink vertex v, a pair of edge-disjoint paths from s to v of minimum total edge cost. Suurballe has given an O(n2 logn)-time algorithm for this problem. We give an implementation of Suurballe's algorithm that runs in O(m log(1+ m/n)n) time and O(m) space. Our algorithm builds an implicit representation of the n pairs of paths; given this representation, the time necessary to explicitly construct the pair of paths for any given sink is O(1) per edge on the paths.Networks 01/1984; 14(2):325-336. · 0.65 Impact Factor

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