The b-matching problem in distance-hereditary graphs and beyond

Guillaume Ducoffe, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We make progress on the fine-grained complexity of Maximum-Cardinality Matching on graphs of bounded clique-width. Quasi linear-time algorithms for this problem have been recently proposed for the important subclasses of bounded-treewidth graphs (Fomin et al., SODA'17) and graphs of bounded modular-width (Coudert et al., SODA'18). We present such algorithm for bounded split-width graphs - a broad generalization of graphs of bounded modular-width, of which an interesting subclass are the distance-hereditary graphs. Specifically, we solve Maximum-Cardinality Matching in O((klog 2 k)·(m+n)·log n)-time on graphs with split-width at most k. We stress that the existence of such algorithm was not even known for distance-hereditary graphs until our work. Doing so, we improve the state of the art (Dragan, WG'97) and we answer an open question of (Coudert et al., SODA'18). Our work brings more insights on the relationships between matchings and splits, a.k.a., join operations between two vertex-subsets in different connected components. Furthermore, our analysis can be extended to the more general (unit cost) b-Matching problem. On the way, we introduce new tools for b-Matching and dynamic programming over split decompositions, that can be of independent interest.

Original languageEnglish
Title of host publication29th International Symposium on Algorithms and Computation, ISAAC 2018
EditorsDer-Tsai Lee, Chung-Shou Liao, Wen-Lian Hsu
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770941
DOIs
Publication statusPublished - Dec 1 2018
Event29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, Taiwan
Duration: Dec 16 2018Dec 19 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume123
ISSN (Print)1868-8969

Conference

Conference29th International Symposium on Algorithms and Computation, ISAAC 2018
CountryTaiwan
CityJiaoxi, Yilan
Period12/16/1812/19/18

Keywords

  • B-matching
  • Distance-hereditary graphs
  • FPT in P
  • Maximum-cardinality matching
  • Split decomposition

ASJC Scopus subject areas

  • Software

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  • Cite this

    Ducoffe, G., & Popa, A. (2018). The b-matching problem in distance-hereditary graphs and beyond. In D-T. Lee, C-S. Liao, & W-L. Hsu (Eds.), 29th International Symposium on Algorithms and Computation, ISAAC 2018 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 123). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2018.30