Matteo Fischetti, Cristiano Saturni (auth.), Michael Jünger,'s Integer Programming and Combinatorial Optimization: 11th PDF

By Matteo Fischetti, Cristiano Saturni (auth.), Michael Jünger, Volker Kaibel (eds.)

ISBN-10: 3540261990

ISBN-13: 9783540261995

ISBN-10: 3540321020

ISBN-13: 9783540321026

Since its commence in 1990, the IPCO convention sequence (held lower than the auspices of theMathematicalProgrammingSociety)hasbecomeanimportantforumforthe presentation of modern ends up in Integer Programming and Combinatorial Op- mization. This quantity compiles the papers offered at IPCO XI, the 11th convention during this sequence, held June 8–10, 2005, on the Technische Universit¨ at Berlin. The excessive curiosity during this convention sequence is clear within the huge variety of submissions. For IPCO XI, 119 prolonged abstracts of as much as 10 pages have been submitted. in the course of its assembly on January 29–30, 2005, this system Committee rigorously chosen 34 contributions for presentation in non-parallel classes on the convention. The ?nal offerings weren't effortless in any respect, for the reason that, end result of the restricted variety of time slots, many first-class papers couldn't be authorized. throughout the choice approach the contributions have been refereed in response to the factors of refereed meetings. because of this strategy, you've on your palms a quantity that includes papers describing top quality examine e?orts. The web page restrict for contributions to this court cases quantity used to be set to fifteen. you could ?nd complete models of the papers in scienti?c journals within the close to destiny. We thank all of the authors who submitted papers. in addition, this system Committee is indebted to the numerous reviewers who, with their speci?c services, helped much in making the decisions.

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Such a laminar collection of T -cuts is guaranteed to exist by Proposition 1 and Observation 1. We claim that whenever X, Y and Z are three distinct elements of F such that X ⊆ Y ⊆ Z or X ⊆ Y and Y ∩ Z = ∅, then T -cuts δ(X) and δ(Z) are fringe-disjoint. It suffices to consider the first case. Suppose there exists an element a ∈ A which belongs to the fringes of X and Z. In particular, a has ¯ If a ∈ Y then ab ∈ δ(Y ) ∩ δ(Z), a a neighbor b in X and a neighbor b in Z. ¯ contradiction. If a ∈ Y then ab ∈ δ(X) ∩ δ(Y ), a contradiction.

Nemhauser Section 5 focuses on some applications of our procedure. In Section 6, we present computational results for nested and disjoint sets to demonstrate the strength of the inequalities in improving linear programming relaxation bounds. Proofs of all results in this paper are provided in [4]. 2 The Pairing Scheme Given a set of non-negative integer vectors X ⊂ Zn+ , a vector a ∈ Rn+1 defines a valid inequality for X if n aj xj − an+1 ≥ 0 for all x ∈ X. j=1 Given two such valid inequalities defined by vectors a and b, the one defined by a dominates the one defined by b if aj ≤ bj for all j = 1, .

IPCO 2005, LNCS 3509, pp. 35–50, 2005. c Springer-Verlag Berlin Heidelberg 2005 36 S. Fiorini et al. relaxations are duals. Letting V denote the vertex set of G and O denote the set of odd cycles in G, these dual LPs are: Covering LP: min yv v∈V Packing LP: max xC C∈O yv ≥ 1 ∀C ∈ O v:v∈C xC ≤ 1 ∀v ∈ V C:v∈C yv ≥ 0 ∀v ∈ V xC ≥ 0 ∀C ∈ O Goemans and Williamson [5] gave a constant factor approximation algorithm for the minimum odd cycle transversal problem in planar graphs using the primaldual method.

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Integer Programming and Combinatorial Optimization: 11th International IPCO Conference, Berlin, Germany, June 8-10, 2005. Proceedings by Matteo Fischetti, Cristiano Saturni (auth.), Michael Jünger, Volker Kaibel (eds.)

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