Why Is Maximum Clique Often Easy in Practice?

Walteros, Jose L.; Buchanan, Austin

doi:10.1287/opre.2019.1970

Cited by 23 publications

(7 citation statements)

References 56 publications

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“…Our implementaton uses dOmega [29] for finding the initial maximum clique, and MiniCSP 6 as the underlying CDCL CSP solver during the I-Dsatur phase. 7 We compare it to the state of the art: the FastColor approach [16].…”

Section: Resultsmentioning

confidence: 99%

A Hybrid Approach for Exact Coloring of Massive Graphs

Hébrard

Katsirelos²

2019

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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The graph coloring problem appears in numerous applications, yet many state-of-the-art methods are hardly applicable to real world, very large, networks. The most efficient approaches for massive graphs rely on "peeling" the graph of its low-degree vertices and focus on the maximum k-core where k is some lower bound on the chromatic number of the graph. However, unless the graphs are extremely sparse, the cores can be very large, and lower and upper bounds are often obtained using greedy heuristics. In this paper, we introduce a combined approach using local search to find good quality solutions on massive graphs as well as locate small subgraphs with potentially large chromatic number. The subgraphs can be used to compute good lower bounds, which makes it possible to solve optimally extremely large graphs, even when they have large k-cores.

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Section: Resultsmentioning

confidence: 99%

A Hybrid Approach for Exact Coloring of Massive Graphs

Hébrard

Katsirelos²

2019

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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“…However, exact algorithms for NP‐hard problems that are able to solve a number of real network instances with millions of nodes to proven optimality, have recently been described (e.g., San Segundo et al., 2016; Walteros and Buchanan. 2020).…”

Section: Discussionmentioning

confidence: 99%

“…One reason for this is that many hard combinatorial problems of practical interest are NP-hard and only approximation methods are able to provide good solutions. However, exact algorithms for NP-hard problems which are able to solve a number of real networks instances with millions of nodes to proven optimality, have recently been described (e.g., San Segundo et al (2016) or Walteros and Buchanan (2020)).…”

Section: Challenges and Prospects Of Exact Algorithmsmentioning

confidence: 99%

Research trends in combinatorial optimization

Weinand

Sörensen

Segundo

et al. 2021

Int Trans Operational Res

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Real‐world problems are becoming highly complex and therefore have to be solved with combinatorial optimization (CO) techniques. Motivated by the strong increase in publications on CO, 8393 articles from this research field are subjected to a bibliometric analysis. The corpus of literature is examined using mathematical methods and a novel algorithm for keyword analysis. In addition to the most relevant countries, organizations, and authors as well as their collaborations, the most pertinent CO problems, solution methods, and application areas are presented. Publications on CO focus mainly on the development or enhancement of metaheuristics like genetic algorithms. The increasingly problem‐oriented studies deal particularly with real‐world applications within the energy sector, production sector, or data management, which are of increasing relevance due to various global developments. The demonstration of global research trends in CO can support researchers in identifying the relevant issues regarding this expanding and transforming research area.

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“…There have been many advances in the search for faster algorithms for maximum cliques, many of which focus on specific domains of graphs [4][5][6][7]. To make the algorithm work fast on general graphs, some good heuristics have been proposed to speed up the branch-and-bound search [1,4,[8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning

et al. 2021

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Finding a maximum clique is important in research areas such as computational chemistry, social network analysis, and bioinformatics. It is possible to compare the maximum clique size between protein graphs to determine their similarity and function. In this paper, improvements based on machine learning (ML) are added to a dynamic algorithm for finding the maximum clique in a protein graph, Maximum Clique Dynamic (MaxCliqueDyn; short: MCQD). This algorithm was published in 2007 and has been widely used in bioinformatics since then. It uses an empirically determined parameter, Tlimit, that determines the algorithm’s flow. We have extended the MCQD algorithm with an initial phase of a machine learning-based prediction of the Tlimit parameter that is best suited for each input graph. Such adaptability to graph types based on state-of-the-art machine learning is a novel approach that has not been used in most graph-theoretic algorithms. We show empirically that the resulting new algorithm MCQD-ML improves search speed on certain types of graphs, in particular molecular docking graphs used in drug design where they determine energetically favorable conformations of small molecules in a protein binding site. In such cases, the speed-up is twofold.

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Why Is Maximum Clique Often Easy in Practice?

Abstract: Jose L. Walteros and Austin Buchanan

Cited by 23 publications

References 56 publications

A Hybrid Approach for Exact Coloring of Massive Graphs

A Hybrid Approach for Exact Coloring of Massive Graphs

Research trends in combinatorial optimization

Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning

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