Query-Driven Maximum Quasi-Clique Search

Lee, Pei; Lakshmanan, Laks V. S.

doi:10.1137/1.9781611974348.59

Cited by 22 publications

(9 citation statements)

References 20 publications

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“…Liu and Wong [14] propose the QUICK algorithm for enumerating all maximal γ-quasi-cliques from a simple undirected graph that uses a number of pruning techniques, some from prior works, and some newly developed. Lee and Lakshmanan [20] study the problem of finding a maximum γ-quasi-clique containing a given subset of vertices S of the original graph, and propose a heuristic algorithm. Recently, Pastukhov et al [15] study the maximum degreebased γ-quasi-clique problem.…”

Section: A Related Workmentioning

confidence: 99%

Enumerating Top-k Quasi-Cliques

Sanei-Mehri

Das

Tirthapura

2018

2018 IEEE International Conference on Big Data (Big Data)

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Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasicliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics 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 if a given quasi-clique is maximal (i.e. not contained within another quasi-clique) is NPhard (2) We present a novel heuristic algorithm KERNELQC to enumerate the k largest quasi-cliques in a graph. Our method is based on identifying kernels of extremely dense subgraphs within a graph, following 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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Section: A Related Workmentioning

confidence: 99%

Enumerating Top-k Quasi-Cliques

Sanei-Mehri

Das

Tirthapura

2018

2018 IEEE International Conference on Big Data (Big Data)

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“…They reported that dense subgraphs in molecular interaction networks correspond to meaningful modules or building blocks of molecular networks such as protein complexes or dynamic functional units. The problem of finding large dense subgraphs have also appeared in a number of other domains including biology [3,9,16,4], social network analysis [10,20,36], finance [5,17,29,30] and data mining [25,32].…”

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confidence: 99%

Dense subgraphs in random graphs

Balister

Bollobás

Sahasrabudhe

et al. 2019

Discrete Applied Mathematics

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For a constant γ ∈ [0, 1] and a graph G, let ω γ (G) be the largest integer k for which there exists a k-vertex subgraph of G with at least γ k 2 edges. We show that if 0 < p < γ < 1 then ω γ (G n,p ) is concentrated on a set of two integers. More precisely, with α(γ, p) = γ log γ p +(1−γ) log 1−γ 1−p , we show that ω γ (G n,p ) is one of the two integers closest to 2 α(γ,p) log n − log log n + log eα(γ,p) 2 + 1 2 , with high probability. While this situation parallels that of cliques in random graphs, a new technique is required to handle the more complicated ways in which these "quasi-cliques" may overlap.

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“…Recently, Guo et al [35] developed parallel algorithms, powered by load balancing techniques, to enumerate maximal quasi-cliques in a distributed framework. Lee and Lakshmanan [42] investigated the problem of finding a maximum γ -quasi-clique containing a given subset of vertices S of the original graph and proposed a heuristic algorithm. Pastukhov et al [55] studied the maximum degree-based γ -quasi-clique problem.…”

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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Query-Driven Maximum Quasi-Clique Search

Cited by 22 publications

References 20 publications

Enumerating Top-k Quasi-Cliques

Enumerating Top-k Quasi-Cliques

Dense subgraphs in random graphs

Mining Largest Maximal Quasi-Cliques

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