Subexponential Algorithms for Partial Cover Problems

Partial Cover problems are optimization versions of fundamental and well studied problems like Vertex Cover and Dominating Set. Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number (k) of vertices, rather than covering all edges (or vertices). In general graphs, these problems are hard for parameterized complexity classes when parameterized by k. It was recently shown by Amini et. al. [FSTTCS 08 ] that Partial Vertex Cover and Partial Dominating Set are fixed parameter tractable on large classes of sparse graphs, namely H-minor free graphs, which include planar graphs and graphs of bounded genus. In particular, it was shown that on planar graphs both problems can be solved in time 2O(k) nO(1) . During the last decade there has been an extensive study on parameterized subexponential algorithms. In particular, it was shown that the classical Vertex Cover and Dominating Set problems can be solved in subexponential time on H-mi...

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
• Keywords: Dominating Set, FSTTCS 2009, Problems, Theoretical Computer Science, Vertex Cover