An extension of adaptive multi-start tabu search for the maximum quasi-clique problem

Djeddi, Youcef; Haddadene, Hacene Ait; Belacel, Nabil

doi:10.1016/j.cie.2019.04.040

Cited by 9 publications

(8 citation statements)

References 21 publications

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“…We evaluate NuQClq on a broad range of classic benchmarks as well as sparse instances, and compare it with three state-of-the-art heuristic algorithms. Since previous works use different instances, we select all used instances from (Pinto et al 2019;Djeddi, Haddadene, and Belacel 2019;Zhou, Benlic, and Wu 2020). To be specific, we consider 289 instances, which are mainly divided into two parts: (1) 187 classic instances from DIMACS benchmark (Johnson 1993) 1 and BHOSLIB benchmark (Xu et al 2007) 2 ; (2) 102 sparse instances whose density is from 0.00014% to 3.869% from Florida Sparse Matrix Collection (Davis and Hu 2011) 3 and Stanford Large Network Dataset Collection (Rossi and Ahmed 2015) 4 .…”

Section: Experimental Evaluationmentioning

confidence: 99%

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NuQClq: An Effective Local Search Algorithm for Maximum Quasi-Clique Problem

Chen

Pan

Wang

et al. 2021

AAAI

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The maximum quasi-clique problem (MQCP) is an important extension of maximum clique problem with wide applications. Recent heuristic MQCP algorithms can hardly solve large and hard graphs effectively. This paper develops an efficient local search algorithm named NuQClq for the MQCP, which has two main ideas. First, we propose a novel vertex selection strategy, which utilizes cumulative saturation information to be a selection criterion when the candidate vertices have equal values on the primary scoring function. Second, a variant of configuration checking named BoundedCC is designed by setting an upper bound for the threshold of forbidding strength. When the threshold value of vertex exceeds the upper bound, we reset its threshold value to increase the diversity of search process. Experiments on a broad range of classic benchmarks and sparse instances show that NuQClq significantly outperforms the state-of-the-art MQCP algorithms for most instances.

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Section: Experimental Evaluationmentioning

confidence: 99%

“…The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21) (2019) had the best performance. Djeddi et al (2019) used an extension of adaptive multistart tabu search to approximate the MQCP solution, resulting in the TSQC algorithm. Very recently, Zhou et.…”

Section: Introductionmentioning

confidence: 99%

NuQClq: An Effective Local Search Algorithm for Maximum Quasi-Clique Problem

Chen

Pan

Wang

et al. 2021

AAAI

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“…Balister et al studied the largest order of γ -quasi-clique and derived the concentration bound on the size of the maximum densitybased δ -quasi-clique. Other exact and heuristic methods for maximum density-based quasi-cliques include [28,47,60].…”

Section: Degree-based and Density-based Quasi-cliquesmentioning

confidence: 99%

Mining Largest Maximal Quasi-Cliques

Sanei-Mehri

Das

Hashemi

et al. 2021

ACM Trans. Knowl. Discov. Data

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Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications in bioinformatics and social network analysis. However, enumerating quasi-cliques in a graph is a challenging problem, even harder than the problem of enumerating cliques. We consider the enumeration of top- k degree-based quasi-cliques and make the following contributions: (1) we show that even the problem of detecting whether a given quasi-clique is maximal (i.e., not contained within another quasi-clique) is NP-hard. (2) We present a novel heuristic algorithm K ernel QC to enumerate the k largest quasi-cliques in a graph. Our method is based on identifying kernels of extremely dense subgraphs within a graph, followed by growing subgraphs around these kernels, to arrive at quasi-cliques with the required densities. (3) Experimental results show that our algorithm accurately enumerates quasi-cliques from a graph, is much faster than current state-of-the-art methods for quasi-clique enumeration (often more than three orders of magnitude faster), and can scale to larger graphs than current methods.

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“…The reader is referred to the survey [4] for an extensive list of references. Some later references to the maximum clique and related problems can be found in [9][10][11][12][13]. When comparable, these later approaches do not always match SBTS or HTS.…”

Section: Introductionmentioning

confidence: 99%

The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

2020

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Let G=(V,E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances.

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An extension of adaptive multi-start tabu search for the maximum quasi-clique problem

Cited by 9 publications

References 21 publications

NuQClq: An Effective Local Search Algorithm for Maximum Quasi-Clique Problem

NuQClq: An Effective Local Search Algorithm for Maximum Quasi-Clique Problem

Mining Largest Maximal Quasi-Cliques

The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

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