The shortest multipaths problem in a capacitated dense channel

Bentz, Cédric; Costa, Marie-Christine; Picouleau, Christophe; Zrikem, Maria

doi:10.1016/j.ejor.2006.03.007

Cited by 2 publications

(1 citation statement)

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“…We first consider the problem of determining a routing with minimum total length: we give a greedy polynomial-time algorithm to solve this problem in particular grids called dense channels. This work, presented in Bentz et al (2007a), extends previous results of Formann et al (1993). Then, we show that MCM and MIMF are polynomial-time solvable in a class of grids with uniform capacity: the algorithms we design are based on a duality relationship and on previous results concerning decision problems associated with MIMF (see Frank 1982;Okamura and Seymour 1981).…”

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confidence: 75%

Exact and approximate resolution of integral multiflow and multicut problems: algorithms and complexity

Bentz

2007

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This is a summary of the author's PhD thesis supervised by MarieChristine Costa and Frédéric Roupin and defended on 20 November 2006 at the Conservatoire National des Arts et Métiers in Paris (France). The thesis is written in French and is available upon request from the author. This work deals with two wellknown optimization problems from graph theory: the maximum integral multiflow and the minimum multicut problems. The main contributions of this thesis concern the polynomial-time solvability and the approximation of these two problems (and of some of their variants) in classical classes of graphs: bounded tree-width graphs, planar graphs and grids, digraphs, etc.

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