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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Bibliographic Details
Published in:Computers & operations research Vol. 38; no. 2; pp. 571 - 581
Main Authors: San Segundo, Pablo, Rodríguez-Losada, Diego, Jiménez, Agustín
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.02.2011
Elsevier
Pergamon Press Inc
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2010.07.019