Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs

Many NP-complete problems on planar graphs are “fixed-parameter tractable:” Recent theoretical work provided tree decomposition based fixed-parameter algorithms exactly solving various parameterized problems on planar graphs, among others Vertex Cover, in time O(c √ kn). Here, c is some constant depending on the graph problem to be solved, n is the number of graph vertices, and k is the problem parameter (for Vertex Cover this is the size of the vertex cover). In this paper, we present an experimental study for such tree decomposition based algorithms focusing on Vertex Cover. We demonstrate that the tree decomposition based approach provides a valuable way of exactly solving Vertex Cover on planar graphs. Doing so, we also demonstrate the impressive power of the so-called Nemhauser/Trotter theorem which provides a Vertex Cover-specific, extremely useful data reduction through polynomial time preprocessing. Altogether, this underpins the practical importance of the underlying theory.