TY - GEN
T1 - Fully polynomial FPT algorithms for some classes of bounded clique-width graphs
AU - Coudert, David
AU - Ducoffe, Guillaume
AU - Popa, Alexandru
N1 - Publisher Copyright:
© Copyright 2018 by SIAM.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
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U2 - 10.1137/1.9781611975031.176
DO - 10.1137/1.9781611975031.176
M3 - Conference contribution
AN - SCOPUS:85045548643
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 2765
EP - 2784
BT - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
A2 - Czumaj, Artur
PB - Association for Computing Machinery
T2 - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Y2 - 7 January 2018 through 10 January 2018
ER -