Annealed replication: a new heuristic for the maximum clique problem

Substructure similarity search is to retrieve graphs that approximately contain a given query graph. It has many applications, e.g., detecting similar functions among chemical compounds. The problem is challenging as even testing subgraph containment between two graphs is NP-complete. Hence, existing techniques adopt the filtering-and-verification framework with the focus on developing effective and efficient techniques to remove non-promising graphs.Nevertheless, existing filtering techniques may be still unable to effectively remove many "low" quality candidates.To resolve this, in this paper we propose a novel indexing technique, GrafD-Index, to index graphs according to their "distances" to features. We characterize a tight condition under which the distance-based triangular inequality holds. We then develop lower and upper bounding techniques that exploit the GrafD-Index to (1) prune non-promising graphs and (2) include graphs whose similarities are guaranteed to exceed the given similarity threshold. Considering that the verification phase is not well studied and plays the dominant role in the whole process, we devise efficient algorithms to verify candidates. A comprehensive experiment using real datasets demonstrates that our proposed methods significantly outperform existing methods.

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“…Related work may be found in [1,2,3,4,7,8,16,14,17]. These techniques are not applicable to MCCS detection.…”

Section: Related Workmentioning

confidence: 99%

Connected substructure similarity search

Shang

Lin

Zhang

et al. 2010

Proceedings of the 2010 ACM SIGMOD International Conference on Management of Data

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“…A systematic investigation of shift-equivariance of StQP-bounds which are closely related to testing copositivity is offered in [8]. Also, the shift perturbation is similar to the regularization approach where the identity matrix I replaces E. For details see [2][3][4].…”

Section: Proposition 32 Let G Be a Graph With Clique Number ω The Mmentioning

confidence: 99%

An improved algorithm to test copositivity

Sponsel

Bundfuss²,

Dür

2011

J Glob Optim

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“…Over the past decades, much effort has been made in devising exact algorithms [17,20,26] as well as powerful heuristics including tabu search [10,18,30], reactive search [5,23,24], stochastic local search [9,15,[22][23][24], variable neighbourhood search [12], ant colony optimization [28] and hybrid methods [27,31]. Most of these approaches have mainly been applied to MCP.…”

Section: Introductionmentioning

confidence: 99%

Breakout Local Search for maximum clique problems

Benlic

Hao

2013

Computers & Operations Research

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The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout Local Search (BLS) which can be applied to both MC and MWC problems without any particular adaptation. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Extensive experimental evaluations using the DIMACS and BOSHLIB benchmarks show that the proposed approach competes favourably with the current state-of-art heuristic methods for MCP. Moreover, it is able to provide some new improved results for a number of MWCP instances. This paper also reports for the first time a detailed landscape analysis, which has been missing in the literature. This analysis not only explains the difficulty of several benchmark instances, but also justifies to some extent the behaviour of the proposed approach and the used parameter settings.

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Annealed replication: a new heuristic for the maximum clique problem

Cited by 49 publications

References 27 publications

Connected substructure similarity search

Connected substructure similarity search

An improved algorithm to test copositivity

Breakout Local Search for maximum clique problems

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