Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution

Abstract. In this paper, we show that algorithms on tree decompositions can be made faster with the use of generalisations of fast subset convolution. Amongst others, this gives algorithms that, for a graph, given with a tree decomposition of width k, solve the dominated set problem in O(nk2 3k ) time and the problem to count the number of perfect matchings in O∗ (2k ) time. Using a generalisation of fast subset convolution, we obtain faster algorithms for all [ρ, σ]-domination problems with finite or cofinite ρ and σ on tree decompositions. These include many well known graph problems. We give additional results on many more graph covering and partitioning problems.

• Type: Conference
• Year: 2009
• Where: ESA
• Authors: Johan M. M. van Rooij, Hans L. Bodlaender, Peter Rossmanith
• Keywords: Algorithms, ESA 2009, Fast Subset Convolution, Tree Decompositions