Partition constrained covering of a symmetric crossing supermodular function by a graph

• Authors: Attila Bernáth;Roland Grappe;Zoltán Szigeti
• Venue: SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
• Year: 2010

Given a symmetric crossing supermodular set function p on V and a partition ρ of V, we solve the problem of finding a graph with ground set V having edges only between the classes of ρ such that for every subset X of V the cut of the graph defined by X contains at least p(X) edges. The objective is to minimize the number of edges of the graph. This problem is a common generalization of the global edge-connectivity augmentation of a graph with partition constraints, which was solved by Bang-Jensen, Gabow, Jordán and Szigeti [1] and the problem of covering a symmetric crossing supermodular set function solved by Benczúr and Frank [3]. Our problem can be considered as an abstract form of the problem of global edge-connectivity augmentation of a hypergraph by a multipartite graph, which was earlier solved by the authors [5].