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

Smith, Derek H.; Montemanni, Roberto; Perkins, Stephanie

doi:10.3390/a13100253

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…Moreover, all the instances for which an optimal solution has been proven in previous studies are left out as well, in consideration of our objective, which is the improvement of state-of-the-art results. This leaves us with a total of 72 instances: 29 of which originally proposed for the graph coloring problem [3] and 43 originally proposed for the maximum clique problem [23].…”

Section: Datasets and Settingsmentioning

confidence: 99%

A Constraint Programming Model for the B-Coloring Problem

Montemanni,

Carraretto,

Mele

et al. 2023

Advances in Transdisciplinary Engineering

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B-coloring is a theoretical optimization problem on a graph that, on top of being used to model some real-world applications, is exploited by some bounding techniques embedded into solvers for the classical graph coloring problem. This implies that improved solutions for the b-coloring problem have an impact on an even larger pool of practical applications modelled by graph coloring in several different fields such as scheduling, timetabling and telecommunications. The b-coloring problem aims to maximize the number of colors used to provide a complete coloring for a graph G = (V,E), while preventing adjacent vertices from receiving the same color. Moreover, each color used is associated to a so-called a b-vertex. A vertex can be a b-vertex only if the set of colors assigned to its adjacent vertices includes all the colors used, apart from the one assigned to the vertex itself. In this work we discuss a new Constraint Programming model for the b-coloring problem and we show how such a paradigm can improve state-of-the-art results for several benchmarks instances commonly adopted in the literature.

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Section: Datasets and Settingsmentioning

confidence: 99%

A Constraint Programming Model for the B-Coloring Problem

Montemanni,

Carraretto,

Mele

et al. 2023

Advances in Transdisciplinary Engineering

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“…The third article in this Special Issue is by Smith, Montemanni and Perkins and focuses on the NP-hard maximum clique problem [3]. This is an important combinatorial optimisation problem that involves identifying the largest subset of vertices that are pairwise adjacent.…”

Section: Algorithms For Graphs and Networkmentioning

confidence: 99%

Editorial for the Special Issue on “Algorithms for Graphs and Networks”

Lewis

2020

Algorithms

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“…Prohibition-based techniques for neighbours are also used in the Reactive Local Search, proposed in [50]. The paper [51] proposes a hybrid algorithm created by combining an exact algorithm with the tabu search. It also uses the relationship between the chromatic number and the maximum clique in the graph.…”

Section: Introductionmentioning

confidence: 99%

The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation

Seda

2023

Symmetry

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The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability for larger instances. Instead of the traditional approaches based on the use of approximate or stochastic heuristic methods, we focus here on the use of integer programming models in the GAMS (General Algebraic Modelling System) environment, which is based on exact methods and sophisticated deterministic heuristics incorporated in it. We propose modifications of integer models, derive their time complexities and show their direct use in GAMS. GAMS makes it possible to find optimal solutions to the maximum clique problem for instances with hundreds of vertices and thousands of edges within minutes at most. For extremely large instances, good approximations of the optimum are given in a reasonable amount of time. A great advantage of this approach over all the mentioned algorithms is that even if GAMS does not find the best known solution within the chosen time limit, it displays its value at the end of the calculation as a reachable bound.

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

Cited by 7 publications

References 17 publications

A Constraint Programming Model for the B-Coloring Problem

A Constraint Programming Model for the B-Coloring Problem

Editorial for the Special Issue on “Algorithms for Graphs and Networks”

The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation

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