Algorithmic Lower Bounds for Problems Parameterized by Clique-width

Many NP-hard problems can be solved efficiently when the input is restricted to graphs of bounded tree-width or clique-width. In particular, by the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the tree-width of the input graph. On the other hand if we restrict ourselves to graphs of clique-width at most t, then there are many natural problems for which the running time of the best known algorithms is of the form nf(t) , where n is the input length and f is some function. It was an open question whether natural problems like GRAPH COLORING, MAX-CUT, EDGE DOMINATING SET, and HAMILTONIAN PATH are fixed parameter tractable when parameterized by the clique-width of the input graph. As a first step toward obtaining lower bounds for clique-width parameterizations, in [SODA 2009 ], we showed that unless FPT=W[1], there is no algorithm with run time O(g(t) ? nc ), for some function g and a co...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtanov, Saket Saurabh
• Keywords: Discrete Algorithms, EDGE DOMINATING SET, Input Graph, Lower Bounds, SODA 2010