Journal ArticleDOI
A new exact maximum clique algorithm for large and massive sparse graphs
TLDR
A new very efficient branch-and-bound exact maximum clique algorithm BBMCSP, designed for large and massive sparse graphs which appear frequently in real life problems from different fields, which improves on recent optimizations proposed in literature for the sparse case such as core-based bounds.About:
This article is published in Computers & Operations Research.The article was published on 2016-02-01. It has received 60 citations till now. The article focuses on the topics: Sparse approximation & Clique.read more
Citations
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An exact algorithm for the maximum clique problem with accelerated pruning
P. Pardalos,L. Gibbons,D. Hearn +2 more
TL;DR: A partially enumerative algorithm is presented for the maximum clique problem which is very simple to implement and Computational results for an efficient implementation on an IBM 3090 computer are provided.
Proceedings ArticleDOI
An Exact Algorithm for the Maximum Weight Clique Problem in Large Graphs
Hua Jiang,Chu Min Li,Felip Manyà +2 more
TL;DR: This work is supported by NSFC Grants No. 61370184, the MeCS platform of the University of Picardie Jules Verne and the HPC platform of Jianghan Univeristy.
Proceedings ArticleDOI
Computing A Near-Maximum Independent Set in Linear Time by Reducing-Peeling
Lijun Chang,Wei Li,Wenjie Zhang +2 more
TL;DR: A Reducing-Peeling framework which iteratively reduces the graph size by applying reduction rules on vertices with very low degrees and temporarily removing the vertex with the highest degree if the reduction rules cannot be applied, and a linear-time algorithm and a near-linear time algorithm that can generate a high-quality independent set from a graph in practice.
Proceedings ArticleDOI
Efficient Maximum Clique Computation over Large Sparse Graphs
TL;DR: An algorithm MC-BRB is designed which transforms an instance of MCC-Sparse to instances of k-clique finding over dense subgraphs (KCF-Dense) that can be computed by the existing MCC -Dense solvers, and a new branch-reduce-&-bound framework for KCF- Dense is developed.
Journal ArticleDOI
SCCWalk: An efficient local search algorithm and its improvements for maximum weight clique problem
TL;DR: Experiments show that the proposed algorithms perform better on classical benchmarks, and obtain the best solutions for most massive graphs, compared to state-of-the-art heuristic algorithms and exact algorithm.
References
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Book ChapterDOI
Reducibility Among Combinatorial Problems
TL;DR: The work of Dantzig, Fulkerson, Hoffman, Edmonds, Lawler and other pioneers on network flows, matching and matroids acquainted me with the elegant and efficient algorithms that were sometimes possible.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Journal ArticleDOI
Algorithm 457: finding all cliques of an undirected graph
Coen Bron,Joep Kerbosch +1 more
TL;DR: Two backtracking algorithms are presented, using a branchand-bound technique [4] to cut off branches that cannot lead to a clique, and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed.
Journal ArticleDOI
Network structure and minimum degree
TL;DR: An approach to network cohesion is proposed that is based on minimum degree and which produces a sequence of subgraphs of gradually increasing cohesion that associates with any network measures of local density which promise to be useful both in characterizing network structures and in comparing networks.
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