New applications of clique separator decomposition for the Maximum Weight Stable Set problem

14Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

Graph decompositions such as decomposition by clique separators and modular decomposition are of crucial importance for designing efficient graph algorithms. Clique separators in graphs were used by Tarjan as a divide-and-conquer approach for solving various problems such as the Maximum Weight Stable Set (MWS) problem, Colouring and Minimum Fill-in. The basic tool is a decomposition tree of the graph whose leaves have no clique separator (so-called atoms), and the problem can be solved efficiently on the graph if it is efficiently solvable on its atoms. We give new examples where the clique separator decomposition works well for the MWS problem; our results improve and extend various recently published results. In particular, we describe the atom structure for some new classes of graphs whose atoms are P5-free (the P5 is the induced path with five vertices) and obtain new polynomial time results for the MWS problem. The complexity of this problem on the class of P5-free graphs is still unknown. © 2006 Elsevier Ltd. All rights reserved.

Cite

CITATION STYLE

APA

Brandstädt, A., Le, V. B., & Mahfud, S. (2007). New applications of clique separator decomposition for the Maximum Weight Stable Set problem. Theoretical Computer Science, 370(1–3), 229–239. https://doi.org/10.1016/j.tcs.2006.10.035

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free