Clique Relaxations in Social Network Analysis: The Maximum <i>k</i>-Plex Problem

Balasundaram, Balabhaskar; Butenko, Sergiy; Hicks, Illya V.

doi:10.1287/opre.1100.0851

Cited by 249 publications

(230 citation statements)

References 45 publications

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“…The experiments of Balasundaram et al (2009) were performed on Dell Precision PWS690 machines with a 2.66 GHz Xeon Processor, 3 GB main memory, implemented using ILOG CPLEX 10.0. The experiments of McClosky and Hicks (2010) were run on a 2.2 GHz Dual-Core AMD Opteron processor with 3 GB main memory.…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, we provide several very effective heuristics (still yielding optimal solution sets) helping to significantly boost the performance of the underlying fixed-parameter algorithms in applications. We perform a number of computational studies, comparing with previous work (Balasundaram et al, 2009;McClosky and Hicks, 2010;Trukhanov, 2008) on exact solutions for k-plex finding which mainly rely on integer linear programming and branch-and-bound. For several real-world graphs, we mostly achieved speedups by orders of magnitude when compared to the previous work.…”

Section: Introductionmentioning

confidence: 99%

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Exact combinatorial algorithms and experiments for finding maximum k-plexes

2011

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We propose new practical algorithms to find maximum-cardinality k-plexes in graphs. A k-plex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most k vertices in the k-plex. Cliques are 1-plexes. In analogy to the special case of finding maximum-cardinality cliques, finding maximum-cardinality k-plexes is NP-hard. Complementing previous work, we develop exact combinatorial algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many real-world graphs outperforming the previously used methods.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact combinatorial algorithms and experiments for finding maximum k-plexes

2011

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“…expanded to actors' relations. Three levels of analysis are to be considered for modeling the supply chain: the triad [28,29]; the group [21,30,31]; and the complete network [29,30].…”

Section: Modeling the Supply Chainmentioning

confidence: 99%

The entry of logistics service provider (LSP) into the wine industry supply chain

Fulconis

Bédé

Saglietto

et al. 2014

BIO Web of Conferences

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Abstract. The purpose of this paper is to study the wine industry supply chain (WSC) organization from a social network approach, with an emphasis on the role of logistics service providers (LSP) could hold in the flow monitoring. We try to understand if LSP can be a substitute to traditional actors for intermediation management. This substitution phenomenon must take account of the wine industry culture that may constitute an obstruction or an accelerator for the development of this activity. We present a conceptual model of the WSC, and we discuss the possible future role of the LSP. This paper introduces a framework contributing to understand worldwide WSC organization, mapping tools and strategies to assess the reasons of their evolution. The cultural impact is underlined in this type of industry showing it could present a boundary to market access for LSP.

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“…3 Merge the instances into one instance of Clique by taking the disjoint union of the graphs. It is clear that this graph contains a clique of given order if and only if one of its connected components does.…”

Section: W[1]-hardness For Parameterization By Degeneracy and Solutiomentioning

confidence: 99%

“…Identifying dense regions of graphs is a fundamental computational problem with many important applications, for instance in computational biology [19] and social network analysis [3]. There are many different definitions of what a dense subgraph is [11,17] and for almost all of these formulations, the corresponding computational problems are NP-hard.…”

Section: Introductionmentioning

confidence: 99%

Finding Dense Subgraphs of Sparse Graphs

Komusiewicz

Sorge

2012

Parameterized and Exact Computation

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Abstract. We investigate the computational complexity of the Densestk-Subgraph (DkS) problem, where the input is an undirected graph G = (V, E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on DkS by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density µ of the sought subgraph, DkS becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixedparameter algorithm for DkS with respect to the combined parameter "degeneracy of G and |V | − k". On the negative side, we find that DkS is W[1]-hard with respect to the combined parameter "solution size k and degeneracy of G". We furthermore strengthen a previous hardness result for DkS [Cai, Comput. J., 2008] by showing that for every fixed µ, 0 < µ < 1, the problem of deciding whether G contains a subgraph of density at least µ is W[1]-hard with respect to the parameter |V | − k.

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Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem

Cited by 249 publications

References 45 publications

Exact combinatorial algorithms and experiments for finding maximum k-plexes

Exact combinatorial algorithms and experiments for finding maximum k-plexes

The entry of logistics service provider (LSP) into the wine industry supply chain

Finding Dense Subgraphs of Sparse Graphs

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