Certifying algorithms for recognizing interval graphs and permutation graphs

Authors:
Dieter Kratsch;Ross M. McConnell;Kurt Mehlhorn;Jeremy P. Spinrad
Affiliations:
Université de Metz, LITA, 57045 Metz Cedex 01, France;Colorado State University, Fort Collins, CO;Max-Planck-Institut für Informatik, Im Stadtwald, Saarbrücken, Germany;Vanderbilt University, Nashville, TN
Venue:
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2003

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Abstract

A certifying algorithm for a decision problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been compromised by a bug in the implementation. We give linear-time certifying algorithms for recognition of interval graphs and permutation graphs. Previous algorithms fail to provide supporting evidence when they claim that the input graph is not a member of the class. We show that our certificates of non-membership can be authenticated in O(|V|) time.