On the boolean-width of a graph: Structure and applications

Isolde Adler, Binh Minh Bui-Xuan, Yuri Rabinovich, Gabriel Renault, Jan Arne Telle, Martin Vatshelle

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Boolean-width is a recently introduced graph invariant. Similar to tree-width, it measures the structural complexity of graphs. Given any graph G and a decomposition of G of boolean-width k, we give algorithms solving a large class of vertex subset and vertex partitioning problems in time O*(2 O(k2)). We relate the boolean-width of a graph to its branch-width and to the boolean-width of its incidence graph. For this we use a constructive proof method that also allows much simpler proofs of similar results on rank-width in [S. Oum. Rank-width is less than or equal to branch-width. Journal of Graph Theory 57(3):239-244, 2008]. For an n-vertex random graph, with a uniform edge distribution, we show that almost surely its boolean-width is Θ(log2 n) - setting boolean-width apart from other graph invariants - and it is easy to find a decomposition witnessing this. Combining our results gives algorithms that on input a random graph on n vertices will solve a large class of vertex subset and vertex partitioning problems in quasi-polynomial time O*(2O(log4 n)).

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 36th International Workshop, WG 2010, Revised Papers
Pages159-170
Number of pages12
DOIs
StatePublished - 2010
Event36th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2010 - Zaros, Crete, Greece
Duration: 28 Jun 201030 Jun 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6410 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference36th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2010
Country/TerritoryGreece
CityZaros, Crete
Period28/06/1030/06/10

Bibliographical note

Funding Information:
Supported by the Norwegian Research Council, projects PARALGO and Graph Searching.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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