International audienceIn this article, we consider the k-edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch-and-Cut algorithm and present some computational results
Given G = (V , E ) an undirected graph and two specified nonadjacent nodes a and b of V , a cut separator is a subset F = δ(C) ⊆ E such that a, b ∈ V \ C and a and b belong to different connected components of the graph induced by V \C. Given a non-negative cost vector c ∈ R |E | + , the cut separator problem is to find a cut separator of minimum cost. This new problem can be seen as a generalization of the vertex separator problem. In this article, we give a polynomial time algorithm for this problem. We also present six equivalent linear programming formulations, and we show their tightness. Using these results we obtain an explicit short polyhedral description of the dominant of the cut separator polytope.
In this paper, a realistic modeling of interferences for frequency assignment in hertzian telecommunication networks is presented. In contrast with traditional interference models based only on binary interference constraints involving two frequencies, this new approach considers the case of cumulative disruptions that are modeled through a unique non‐binary constraint. To deal with these complex constraints, we propose extensions of classical integer linear programming formulations. On a set of realistic instances, we propose hybrid constraint programming and large neighborhood search solution methods to solve minimum interference and minimum span frequency assignment problems. We compare their performances with those of existing heuristics. Finally, we show how the end‐user benefits from using the cumulative model instead of the traditional one.
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