The Multi-terminal Vertex Separator Problem: Polytope Characterization and TDI-ness
نویسندگان
چکیده
In this paper we discuss a variant of the well-known k-separator problem. Consider the simple graph G = (V ∪T,E) with V ∪T the set of vertices, where T is a set of distinguished vertices called terminals, inducing a stable set and E a set of edges. Given a weight function w : V → N, the multi-terminal vertex separator problem consists in finding a subset S ⊆ V of minimum weight intersecting every path between two terminals. We characterize the convex hull of the solutions of this problem in two classes of graph which we call, star trees and clique stars. We also give TDI systems for the problem in these graphs.
منابع مشابه
The multi-terminal vertex separator problem : Complexity, Polyhedra and Algorithms. (Le problème du séparateur de poids minimum : Complexité, Polyèdres et Algorithmes)
This thesis deals with the multi-terminal vertex separator problem. Given a graph G = (V ∪T,E) with V ∪T the set of vertices, where T is a set of terminals, and a weight function w : V → Z, associated with nonterminal nodes, the multi-terminal vertex separator problem consists in partitioning V ∪T into k+1 subsets {S, V1, . . . , Vk} such that there is no edge between two different subsets Vi a...
متن کاملThe Multi-terminal Vertex Separator Problem: Polyhedral Analysis and Branch-and- Cut
Let G = (V ∪ T, E) be an undirected graph such that V is a set of vertices, E a set of edges and T a set of terminal vertices. The Multi-terminal vertex separator problem consists in partitioning V into k + 1 subsets {S, V1,..., Vk} minimizing the size of S and such that there is no edge between two subsets Vi and Vj and each subset Vi contains exactly one terminal. Set S is called a separator....
متن کاملThe cut separator problem
Given G = (V, E) an undirected graph and two speci ed 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 di erent connected components of the graph induced by V \C. Given a nonnegative cost vector c ∈ R|E| + , the optimal cut separator problem is to nd a cut separator of minimum cost. This new problem is closely related to the v...
متن کاملA TDI Description of Restricted 2-Matching Polytopes
We give a TDI description for a class of polytopes which corresponds to a restricted 2-matching problem. The perfect matching polytope, triangle-free perfect 2-matching polytope and relaxations of the traveling salesman polytope are members of this class. For a class of restrictions G. Cornuéjols, D. Hartvigsen and W.R. Pulleyblank have shown that the unweighted problem is tractable; here we sh...
متن کاملOn the Graph of the Pedigree Polytope
Pedigree polytopes are extensions of the classical Symmetric Traveling Salesman Problem polytopes whose graphs (1-skeletons) contain the TSP polytope graphs as spanning subgraphs. While deciding adjacency of vertices in TSP polytopes is coNP-complete, Arthanari has given a combinatorial (polynomially decidable) characterization of adjacency in Pedigree polytopes. Based on this characterization,...
متن کامل