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...

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Fedor V. Fomin, Daniel Lokshtanov, Fabrizio Grandoni, Saket Saurabh
• Keywords: Degree Spanning Tree, Information Retrieval, LATIN 2010, Parameterized Algorithm, Spanning Tree