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Communication Dans Un Congrès Année : 2018

The use of a pruned modular decomposition for Maximum Matching algorithms on some graph classes

Résumé

We address the following general question: given a graph class ${\cal C}$ on which we can solve Maximum Matching in (quasi) linear time, does the same hold true for the class of graphs that can be modularly decomposed into ${\cal C}$ ? As a way to answer this question for distance-hereditary graphs and some other superclasses of cographs, we study the combined effect of modular decomposition with a pruning process over the quotient subgraphs. We remove sequentially from all such subgraphs their so-called one-vertex extensions (i.e., pendant, anti-pendant, twin, universal and isolated vertices). Doing so, we obtain a "pruned modular decomposition", that can be computed in quasi linear time. Our main result is that if all the pruned quotient subgraphs have bounded order then a maximum matching can be computed in linear time. The latter result strictly extends a recent framework in (Coudert et al., SODA'18). Our work is the first to explain why the existence of some nice ordering over the modules of a graph, instead of just over its vertices, can help to speed up the computation of maximum matchings on some graph classes.
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Dates et versions

hal-01955985 , version 1 (14-12-2018)

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Guillaume Ducoffe, Alexandru Popa. The use of a pruned modular decomposition for Maximum Matching algorithms on some graph classes. 29th International Symposium on Algorithms and Computation (ISAAC 2018), Dec 2018, Jiaoxi, Yilan County, Taiwan. ⟨10.4230/LIPIcs.ISAAC.2018.144⟩. ⟨hal-01955985⟩
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