T-colorings of graphs: recent results and open problems
Discrete Mathematics - Special issue: advances in graph labelling
On the use of some known methods for T-colorings of graphs
Annals of Operations Research - Special issue on Tabu search
Discrete Applied Mathematics - ARIDAM IV and V
Tabu Search for Frequency Assignment in Mobile Radio Networks
Journal of Heuristics
The complexity of the T-coloring problem for graphs with small degree
Discrete Applied Mathematics
Stochastic Local Search: Foundations & Applications
Stochastic Local Search: Foundations & Applications
Heuristic methods for graph coloring problems
Proceedings of the 2005 ACM symposium on Applied computing
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The graph set T-colouring problem (GSTCP) is a generalisation of the classical graph colouring problem and it is used to model, for example, the assignment of frequencies in mobile networks. The GSTCP asks for the assignment of sets of nonnegative integers to the vertices of a graph so that constraints on the separation of any two numbers assigned to a single vertex or to adjacent vertices are satisfied and some objective function is optimised. Among the various objective functions of interest, we focus on the minimisation of the span, that is, the difference between the largest and the smallest integers used. In practical applications large size instances of the GSTCP are to be solved and heuristic algorithms become necessary. In this article, we propose a new hybrid procedure for the solution of the GSTCP that combines a known tabu search algorithm with an algorithm for the enumeration of all feasible re-assignments of colours to a vertex. We compare the new algorithm with the basic tabu search algorithm and for both we study possible variants. The experimental comparison, supported by statistical analysis, establishes that the new hybrid algorithm performs better on a variety of instance classes.