منابع مشابه
The Vertex k-cut Problem
Given an undirected graph G = (V,E), a vertex k-cut of G is a vertex subset of V the removing of which disconnects the graph in at least k connected components. Given a graph G and an integer k ≥ 2, the vertex k-cut problem consists in finding a vertex k-cut of G of minimum cardinality. We first prove that the problem is NP-hard for any fixed k ≥ 3. We then present a compact formulation, and an...
متن کاملThe min-cut and vertex separator problem
We consider graph three-partitions with the objective of minimizing the number of edges between the first two partition sets while keeping the size of the third block small. We review most of the existing relaxations for this min-cut problem and focus on a new class of semidefinite relaxations, based on matrices of order 2n+ 1 which provide a good compromise between quality of the bound and com...
متن کاملThe Steiner k-Cut Problem
We consider the Steiner k-cut problem which generalizes both the k-cut problem and the multiway cut problem. The Steiner k-cut problem is defined as follows. Given an edge-weighted undirected graph G = (V,E), a subset of vertices X ⊆ V called terminals, and an integer k ≤ |X|, the objective is to find a minimum weight set of edges whose removal results in k disconnected components, each of whic...
متن کاملThe Capacitated max-k-cut Problem
We consider a capacitated max k-cut problem in which a set of vertices is partitioned into k subsets. Each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that maximizes the sum of edge weights across all pairs of vertices that lie in different subsets. We describe a local-search algo...
متن کاملOn the k - cut problem Francisco Barahona
Given a graph with nonnegative edge-weights, let f(k) be the value of an optimal solution of the k-cut problem. We study f as a function of k. Let g be the convex envelope of f. We give a polynomial algorithm to compute g. In particular, if f is convex, then it can be computed in polynomial time for all k. We show some experiments in computing g. c © 2000 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Optimization
سال: 2019
ISSN: 1572-5286
DOI: 10.1016/j.disopt.2018.07.003