Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice, state-of-the-art methods are based on different approaches, and the empi...

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Vydáno v:Theoretical computer science Ročník 609; s. 211 - 225
Hlavní autoři: Akiba, Takuya, Iwata, Yoichi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 04.01.2016
Témata:
Algorithms
Branch-and-reduce
Complexity
Empirical analysis
Exact exponential algorithms
FPT algorithms
Reduction
State of the art
Vertex cover
Vertex cover
Exact exponential algorithms
Branch-and-reduce
FPT algorithms
ISSN:0304-3975, 1879-2294
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Shrnutí:We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice, state-of-the-art methods are based on different approaches, and the empirical efficiency of such theoretical algorithms has seldom been investigated probably because they are seemingly inefficient because of the plethora of complex reduction rules. In this paper, we design a branch-and-reduce algorithm for the vertex cover problem using the techniques developed for theoretical algorithms and compare its practical performance with other state-of-the-art empirical methods. The results indicate that branch-and-reduce algorithms are actually quite practical and competitive with other state-of-the-art approaches for several kinds of instances, thus showing the practical impact of theoretical research on branching algorithms.
Bibliografie:ObjectType-Article-1
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.09.023