Fully polynomial FPT algorithms for some classes of bounded clique-width graphs

David Coudert, Guillaume Ducoffe, Alexandru Popa

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

14 Citations (Scopus)

Abstract

Recently, hardness results for problems in P were achieved using reasonable complexity theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these assumptions, many graph theoretic problems do not admit truly subquadratic algorithms. A central technique used to tackle the difficulty of the above mentioned problems is fixed-parameter algorithms with polynomial dependency in the fixed parameter (P-FPT). Applying this technique to clique-width, an important graph parameter, remained to be done. In this paper we study several graph theoretic problems for which hardness results exist such as cycle problems, distance problems and maximum matching. We give hardness results and P-FPT algorithms, using clique-width and some of its upper-bounds as parameters. We believe that our most important result is an O(k4 · n + m)-time algorithm for computing a maximum matching where k is either the modular-width or the P4-sparseness. The latter generalizes many algorithms that have been introduced so far for specific subclasses such as cographs. Our algorithms are based on preprocessing methods using modular decomposition and split decomposition. Thus they can also be generalized to some graph classes with unbounded clique-width.

Original languageEnglish
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
PublisherAssociation for Computing Machinery
Pages2765-2784
Number of pages20
ISBN (Electronic)9781611975031
DOIs
Publication statusPublished - Jan 1 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: Jan 7 2018Jan 10 2018

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
CountryUnited States
CityNew Orleans
Period1/7/181/10/18

    Fingerprint

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Coudert, D., Ducoffe, G., & Popa, A. (2018). Fully polynomial FPT algorithms for some classes of bounded clique-width graphs. In A. Czumaj (Ed.), 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 (pp. 2765-2784). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.176