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Canonizing Graphs of Bounded Tree Width in Logspace

Authors Michael Elberfeld, Pascal Schweitzer

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Michael Elberfeld
Pascal Schweitzer

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Michael Elberfeld and Pascal Schweitzer. Canonizing Graphs of Bounded Tree Width in Logspace. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.32

Abstract

Graph canonization is the problem of computing a unique representative, a canon, from the isomorphism class of a given graph. This implies that two graphs are isomorphic exactly if their canons are equal. We show that graphs of bounded tree width can be canonized in deterministic logarithmic space (logspace). This implies that the isomorphism problem for graphs of bounded tree width can be decided in logspace. In the light of isomorphism for trees being hard for the complexity class logspace, this makes the ubiquitous classes of graphs of bounded tree width one of the few classes of graphs for which the complexity of the isomorphism problem has been exactly determined.
Keywords
  • algorithmic graph theory
  • computational complexity
  • graph isomorphism
  • logspace
  • tree width

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