Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution
Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution
复制标题
DOI：
10.1007/978-3-642-04128-0_51
复制
发表时间：
2009-09
期刊：
影响因子：
--
通讯作者：
Johan M. M. van Rooij-Johan-M.-M.-van-Rooij-1796712;H. Bodlaender;P. Rossmanith
中科院分区：
文献类型：
--
作者：
Johan M. M. van Rooij-Johan-M.-M.-van-Rooij-1796712;H. Bodlaender;P. Rossmanith
在本文中，我们表明，树分解的算法可以更快地使用概括的快速子集卷积。除其他外，这给出了算法，对于一个图，给定一个树分解的宽度，解决thedordinated集问题在O（nk 23 k）的时间和问题，以计数完美匹配的数量在O（2k）的时间。利用快速子集卷积的推广，我们得到了树分解上所有ρ和σ为有限或上有限的[ρ，σ]-控制问题的快速算法.其中包括许多著名的图形问题。我们给更多的图覆盖和分区问题的额外结果。
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 widthk, solve thedominated setproblem inO(nk23k) time and the problem to count the number of perfect matchings inO∗(2k) time. Using a generalisation of fast subset convolution, we obtain faster algorithms for all [ρ,σ]-domination problems with finite or cofiniteρandσon tree decompositions. These include many well known graph problems. We give additional results on many more graph covering and partitioning problems.