Using tabu search techniques for graph coloring

Hertz, Alain; Werra, Dominique de

doi:10.1007/bf02239976

Cited by 558 publications

(289 citation statements)

References 3 publications

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“…We use the coloring heuristic present in the Boost Graph Library (BGL), which is an implementation of the algorithm presented in Coleman and More (1984). A better performance could be obtained by using more sophisticated heuristics as, for instance, that proposed in Leighton (1979) or Hertz and de Werra (1987).…”

Section: Preprocessingmentioning

confidence: 99%

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Gualandi

Malucelli

2012

INFORMS Journal on Computing

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We consider two approaches for solving the classical minimum vertex coloring problem, that is the problem of coloring the vertices of a graph so that adjacent vertices have different colors, minimizing the number of used colors, namely Constraint Programming and Column Generation. Constraint Programming is able to solve very efficiently many of the benchmarks, but suffers from the lack of effective bounding methods.On the contrary, Column Generation provides tight lower bounds by solving the fractional vertex coloring problem exploited in a Branch-and-Price algorithm, as already proposed in the literature. The Column Generation approach is here enhanced by using Constraint Programming to solve the pricing subproblem and to compute heuristic solutions. Moreover new techniques are introduced to improve the performance of the Column Generation approach in solving both the linear relaxation and the integer problem. We report extensive computational results applied to the benchmark instances: we are able to prove optimality of 11 new instances, and to improve the best known lower bounds on other 17 instances. Moreover we extend the solution approaches to a generalization of the problem known as Minimum Vertex Graph Multicoloring Problem where a given number of colors has to be assigned to each vertex.

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Section: Preprocessingmentioning

confidence: 99%

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Gualandi

Malucelli

2012

INFORMS Journal on Computing

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“…First, it points out that in practice, one can use known heuristics for graph coloring in choosing the number of clusters. Although the coloring problem is known to be hard to approximate in the worst-case [Feige and Kilian 1998], heuristics that work well in practice are known ( [Hertz andde Werra 1987, Campers et al 1987]). In addition, the reduction also points out that the following two special cases of the CL-feasibility problem can be solved efficiently.…”

Section: Efficiently Solvable Special Cases Of Cl-feasibilitymentioning

confidence: 99%

The complexity of non-hierarchical clustering with instance and cluster level constraints

Davidson

Ravi

2007

Data Min Knowl Disc

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Recent work has looked at extending clustering algorithms with instance level must-link (ML) and cannot-link (CL) background information. Our work introduces δ and ǫ cluster level constraints that influence inter-cluster distances and cluster composition. The addition of background information, though useful at providing better clustering results, raises the important feasibility question: Given a collection of constraints and a set of data, does there exist at least one partition of the data set satisfying all the constraints? We study the complexity of the feasibility problem for each of the above constraints separately and also for combinations of constraints. Our results clearly delineate combinations of constraints for which the feasibility problem is computationally intractable (i.e., NP-complete) from those for which the problem is efficiently solvable (i.e., in the computational class P).We also consider the ML and CL constraints in conjunctive and disjunctive normal forms (CNF and DNF respectively). We show that for ML constraints, the feasibility problem is intractable for CNF but efficiently solvable for DNF. Unfortunately, for CL constraints, the feasibility problem is intractable for both CNF and DNF. This effectively means that CLconstraints in a non-trivial form cannot be efficiently incorporated into clustering algorithms. To overcome this, we introduce the notion of a choice-set of constraints and prove that the feasibility problem for choice-sets is efficiently solvable for both ML and CL constraints. We also present empirical results which indicate that the feasibility problem occurs extensively in real world problems.

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“…This is achieved using the TABUCOL algorithm of Hertz and de Werra [9,7] which, while perhaps not as powerful as more contemporary graph colouring algorithms, does have the advantage of being very fast (see [10] for further details). In essence, TABUCOL uses the tabu search metaheuristic to make a series of small changes (moves) to the candidate solution, attempting to find a solution for which the cost function f 1 = 0 (using G ).…”

Section: Stagementioning

confidence: 99%

Creating seating plans: a practical application

Lewis

Carroll

2016

Journal of the Operational Research Society

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This paper examines the interesting problem of designing seating plans for large events such as weddings and gala dinners where, amongst other things, the aim is to construct solutions where guests are sat on the same tables as friends and family but, perhaps more importantly, are kept away from those they dislike. This problem is seen to be N P-complete from a number of different perspectives. We describe the problem model and heuristic algorithm that is used on the commercial website www.weddingseatplanner.com. We present results on the performance of this algorithm, demonstrating the factors that can influence run time and solution quality, and also present a comparison with an equivalent IP model used in conjunction with a commercial solver.

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Using tabu search techniques for graph coloring

Cited by 558 publications

References 3 publications

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

The complexity of non-hierarchical clustering with instance and cluster level constraints

Creating seating plans: a practical application

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