Initial Sorting of Vertices in the Maximum Clique Problem Reviewed

Segundo, Pablo San; Lopez, Alvaro; Batsyn, Mikhail

doi:10.1007/978-3-319-09584-4_12

Cited by 9 publications

(6 citation statements)

References 19 publications

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“…For many of the DIMACS graphs the degrees of most vertices are fairly similar. This has lead to sophisticated tie-breaking mechanisms based upon the sum of neighbouring degrees (Tomita and Kameda, 2007;San Segundo et al, 2014); Prosser's computational study suggests that sometimes these help, and sometimes they make things worse (Prosser, 2012). We consider the possibility that using parallelism to avoid a strong commitment to the first choice made by a weak early heuristic may be a more fruitful alternative than trying to wring even more information out of the graph at the top of search.…”

Section: The Quality Of Heuristics and What This Impliesmentioning

confidence: 99%

The Shape of the Search Tree for the Maximum Clique Problem and the Implications for Parallel Branch and Bound

McCreesh

Prosser

2015

ACM Trans. Parallel Comput.

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Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel explanation as to why they are successful. We show that load balance is sometimes a problem, but that the interaction of parallel search order and the most likely location of solutions within the search space is often the dominating consideration. We use this explanation to propose a new low-overhead, scalable work splitting mechanism. Our approach uses explicit early diversity to avoid strong commitment to the weakest heuristic advice, and late resplitting for balance. More generally, we argue that for branch and bound, parallel algorithm design should not be performed independently of the underlying sequential algorithm.

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Section: The Quality Of Heuristics and What This Impliesmentioning

confidence: 99%

The Shape of the Search Tree for the Maximum Clique Problem and the Implications for Parallel Branch and Bound

McCreesh

Prosser

2015

ACM Trans. Parallel Comput.

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“…[12] [29]), but almost never refer to core-based orderings. The reason is that cores tend to be of high order in dense small or middle size graphs and become useless as clique bounds.…”

Section: Return Gmentioning

confidence: 96%

A new exact maximum clique algorithm for large and massive sparse graphs

Segundo

Lopez

Pardalos

2016

Computers & Operations Research

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“…We use the bit-parallel algorithm introduced by San Segundo et al [47], with the k min parameter set to 0, so we do not describe it here. We use a simple static degree ordering; other initial vertex orderings have been considered on general clique problems [38,43], and it is possible that special properties of the association graph could be exploited in this step (for example, it is always possible to colour the initial association graph using min(|V(G 1 )| , |V(G 2 )|) colours, but with certain vertex orderings, a greedy sequential colouring will sometimes use many more colours).…”

Section: Ensuring Connectedness In a Clique-based Approachmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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Abstract. The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

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Initial Sorting of Vertices in the Maximum Clique Problem Reviewed

Cited by 9 publications

References 19 publications

The Shape of the Search Tree for the Maximum Clique Problem and the Implications for Parallel Branch and Bound

The Shape of the Search Tree for the Maximum Clique Problem and the Implications for Parallel Branch and Bound

A new exact maximum clique algorithm for large and massive sparse graphs

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

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