Integer solution to synthesis of communication networks
Mathematics of Operations Research
Optimal wavelength-routed multicasting
Discrete Applied Mathematics
Parametric min-cuts analysis in a network
Discrete Applied Mathematics
Multi-terminal multipath flows: synthesis
Discrete Applied Mathematics
Integer version of the multipath flow network synthesis problem
Discrete Applied Mathematics
Region growing for multi-route cuts
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An improved algorithm for decomposing arc flows into multipath flows
Operations Research Letters
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For improving reliability of communication in communication networks, where edges are subject to failure, Kishimoto [Reliable flow with failures in a network, IEEE Trans. Reliability, 46 (1997) 308-315] defined a @d-reliable flow, for a given source-sink pair of nodes, in a network for @d@?(0,1], where no edge carries a flow more than a fraction @d of the total flow in the network, and proved a max-flow min-cut theorem with cut-capacites defined suitably. Kishimoto and Takeuchi in [A method for obtaining @d-reliable flow in a network, IECCE Fundamentals E-81A (1998) 776-783] provided an efficient algorithm for finding such a flow. When (1/@d) is an integer, say q, Kishimoto and Takeuchi [On m-route flows in a network, IEICE Trans. J-76-A (1993) 1185-1200 (in Japanese)] introduced the notion of a q-path flow. Kishimoto [A method for obtaining the maximum multi-route flows in a network, Networks 27 (1996) 279-291] proved a max-flow min-cut theorem for q-path flow between a given source-sink pair (s,t) of nodes and provided a strongly polynomial algorithm for finding a q-path flow from s to t of maximum flow-value. In this paper, we extend the concept of q-path flow to any real number q=1. When q(=1/@d) is fractional, we show that this general q-path flow can be viewed as a sum of some q-path flow and some q-path flow. We discuss several applications of this results, which include a simpler proof and generalization of a known result on wavelength division multiplexing problem. Finally we present a strongly polynomial, combinatorial algorithm for synthesizing an undirected network with minimum sum of edge capacities that satisfies (non-simultaneously) specified minimum requirements of q-path flow-values between all pairs of nodes, for a given real number q=1.