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Journal Articles Algorithmica Year : 2014

Practical and Efficient Circle Graph Recognition

Abstract

Circle graphs are the intersection graphs of chords in a circle. This paper presents the first sub-quadratic recognition algorithm for the class of circle graphs. Our algorithm is O(n + m) times the inverse Ackermann function, α(n + m), whose value is smaller than 4 for any practical graph. The algorithm is based on a new in- cremental Lexicographic Breadth-First Search characterization of circle graphs, and a new efficient data-structure for circle graphs, both developed in the paper. The al- gorithm is an extension of a Split Decomposition algorithm with the same running time developed by the authors in a companion paper.

Dates and versions

lirmm-00805194 , version 1 (27-03-2013)

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Emeric Gioan, Christophe Paul, Marc Tedder, Derek Corneil. Practical and Efficient Circle Graph Recognition. Algorithmica, 2014, 69 (4), pp.759-788. ⟨10.1007/s00453-013-9745-8⟩. ⟨lirmm-00805194⟩
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