Detecting 2-joins faster

Authors:
Pierre Charbit;Michel Habib;Nicolas Trotignon;Kristina VušKović
Affiliations:
Université Paris 7, LIAFA, Case 7014, 75205 Paris Cedex 13, France;Université Paris 7, LIAFA, Project team Inria: Gang, Case 7014, 75205 Paris Cedex 13, France;CNRS, LIP ENS de Lyon, INRIA, Université de Lyon, 15 parvis René Descartes, BP 7000, 69342 Lyon cedex 07, France;School of Computing, University of Leeds, Leeds LS2 9JT, UK and Faculty of Computer Science, Union University, Knez Mihailova 6/VI, 11000 Belgrade, Serbia
Venue:
Journal of Discrete Algorithms
Year:
2012

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Abstract

2-Joins are edge cutsets that naturally appear in the decomposition of several classes of graphs closed under taking induced subgraphs, such as balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free graphs. Their detection is needed in several algorithms, and is the slowest step for some of them. The classical method to detect a 2-join takes O(n^3m) time where n is the number of vertices of the input graph and m is the number of its edges. To detect non-path 2-joins (special kinds of 2-joins that are needed in all of the known algorithms that use 2-joins), the fastest known method takes time O(n^4m). Here, we give an O(n^2m)-time algorithm for both of these problems. A consequence is a speed-up of several known algorithms.