An exact bit-parallel algorithm for the maximum clique problem

This paper presents a new exact maximum clique algorithm which improves the bounds obtained in state of the art approximate coloring by reordering the vertices at each step. Moreover, the algorithm can make full use of bit strings to sort vertices in constant time as well as to compute graph transit...

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Vydané v:	Computers & operations research Ročník 38; číslo 2; s. 571 - 581
Hlavní autori:	San Segundo, Pablo, Rodríguez-Losada, Diego, Jiménez, Agustín
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier Ltd 01.02.2011 Elsevier Pergamon Press Inc
Predmet:	Algorithms Applied sciences Approximation Bit string Bit-parallelism Branch & bound algorithms Branch and bound Central processing units Coloring Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Exact sciences and technology Graph coloring Graph theory Graphs Information retrieval. Graph Mathematics Maximum clique Operations research Registers Sciences and techniques of general use State of the art Strings Studies Theoretical computing Coloring Bit string Bit-parallelism Branch and bound Maximum clique Binary sequence Parallel algorithm Branch and bound method Graph clique Parallelism Graph theory Central unit
ISSN:	0305-0548, 1873-765X, 0305-0548
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Abstract	This paper presents a new exact maximum clique algorithm which improves the bounds obtained in state of the art approximate coloring by reordering the vertices at each step. Moreover, the algorithm can make full use of bit strings to sort vertices in constant time as well as to compute graph transitions and bounds efficiently, exploiting the ability of CPUs to process bitwise operations in blocks of size the ALU register word. As a result it significantly outperforms a current leading algorithm.
AbstractList	This paper presents a new exact maximum clique algorithm which improves the bounds obtained in state of the art approximate coloring by reordering the vertices at each step. Moreover, the algorithm can make full use of bit strings to sort vertices in constant time as well as to compute graph transitions and bounds efficiently, exploiting the ability of CPUs to process bitwise operations in blocks of size the ALU register word. As a result it significantly outperforms a current leading algorithm. This paper presents a new exact maximum clique algorithm which improves the bounds obtained in state of the art approximate coloring by reordering the vertices at each step. Moreover, the algorithm can make full use of bit strings to sort vertices in constant time as well as to compute graph transitions and bounds efficiently, exploiting the ability of CPUs to process bitwise operations in blocks of size the ALU register word. As a result it significantly outperforms a current leading algorithm. [PUBLICATION ABSTRACT]
Author	San Segundo, Pablo Jiménez, Agustín Rodríguez-Losada, Diego
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SubjectTerms	Algorithms Applied sciences Approximation Bit string Bit-parallelism Branch & bound algorithms Branch and bound Central processing units Coloring Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Exact sciences and technology Graph coloring Graph theory Graphs Information retrieval. Graph Mathematics Maximum clique Operations research Registers Sciences and techniques of general use State of the art Strings Studies Theoretical computing
Title	An exact bit-parallel algorithm for the maximum clique problem
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