Sciweavers

Share
LATIN
2010
Springer

Sharp Separation and Applications to Exact and Parameterized Algorithms

9 years 7 months ago
Sharp Separation and Applications to Exact and Parameterized Algorithms
Many divide-and-conquer algorithms employ the fact that the vertex set of a graph of bounded treewidth can be separated in two roughly balanced subsets by removing a small subset of vertices, referred to as a separator. In this paper we prove a trade-off between the size of the separator and the sharpness with which we can fix the size of the two sides of the partition. Our result appears to be a handy and powerful tool for the design of exact and parameterized algorithms for NP-hard problems. We illustrate that by presenting two applications. Our first application is a parameterized algorithm with running time O(16k+o(k) + nO(1) ) for the Maximum Internal Subtree problem in directed graphs. This is a significant improvement over the best previously known parameterized algorithm for the problem by [Cohen et al.’09], running in time O(49.4k + nO(1) ). The second application is a O(2n+o(n) ) time algorithm for the Degree Constrained Spanning Tree problem: find a spanning tree of a...
Fedor V. Fomin, Daniel Lokshtanov, Fabrizio Grando
Added 18 May 2010
Updated 18 May 2010
Type Conference
Year 2010
Where LATIN
Authors Fedor V. Fomin, Daniel Lokshtanov, Fabrizio Grandoni, Saket Saurabh
Comments (0)
books