research-article

Fully Polynomial FPT Algorithms for Some Classes of Bounded Clique-width Graphs

Authors:

Guillaume Ducoffe,

Alexandru PopaAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 15, Issue 3

Article No.: 33, Pages 1 - 57

https://doi.org/10.1145/3310228

Published: 07 June 2019 Publication History

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 article, 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 algorithm in O(k⁴ ⋅ n + m)-time for computing a maximum matching, where k is either the modular-width of the graph 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.

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Index Terms

Fully Polynomial FPT Algorithms for Some Classes of Bounded Clique-width Graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
      2. Matchings and factors
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Design and analysis of algorithms
    1. Graph algorithms analysis
    2. Parameterized complexity and exact algorithms
      1. Fixed parameter tractability

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 15, Issue 3

July 2019

392 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3331056

Editor:
Aravind Srinivasan
University of Maryland, USA

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Publication History

Published: 07 June 2019

Accepted: 01 January 2019

Revised: 01 January 2019

Received: 01 April 2018

Published in TALG Volume 15, Issue 3

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https://doi.org/10.1016/j.jcss.2024.103606
Korhonen TSokołowski MMohar BShinkar IO'Donnell R(2024)Almost-Linear Time Parameterized Algorithm for Rankwidth via Dynamic RankwidthProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649732(1538-1549)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649732
Ortali GTollis I(2024)A fixed-parameter algorithm for dominance drawings of DAGsTheoretical Computer Science10.1016/j.tcs.2024.1148191020:COnline publication date: 12-Dec-2024
https://dl.acm.org/doi/10.1016/j.tcs.2024.114819
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