The most vital nodes with respect to independent set and vertex cover |
| |
Authors: | Cristina Bazgan Sonia ToubalineZsolt Tuza |
| |
Institution: | a Université Paris-Dauphine, LAMSADE, Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, Franceb Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungaryc Department of Computer Science and Systems Technology, University of Pannonia, H-8200 Veszprém, Egyetem u. 10, Hungary |
| |
Abstract: | Given an undirected graph with weights on its vertices, the k most vital nodes independent set (k most vital nodes vertex cover) problem consists of determining a set of k vertices whose removal results in the greatest decrease in the maximum weight of independent sets (minimum weight of vertex covers, respectively). We also consider the complementary problems, minimum node blocker independent set (minimum node blocker vertex cover) that consists of removing a subset of vertices of minimum size such that the maximum weight of independent sets (minimum weight of vertex covers, respectively) in the remaining graph is at most a specified value. We show that these problems are NP-hard on bipartite graphs but polynomial-time solvable on unweighted bipartite graphs. Furthermore, these problems are polynomial also on cographs and graphs of bounded treewidth. Results on the non-existence of ptas are presented, too. |
| |
Keywords: | Most vital vertices Independent set Vertex cover Time complexity NP-hard Bipartite graph Bounded treewidth Cograph |
本文献已被 ScienceDirect 等数据库收录! |
|