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(n k 2 3 k ) time and the problem to count the number of perfect matchings in O ∗ (2 k ) 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.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call