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An exact algorithm for the edge coloring by total labeling problem. (English) Zbl 1439.05080
Summary: This paper addresses the edge coloring by total labeling graph problem. This is a labeling of the vertices and edges of a graph such that the weights (colors) of the edges, defined by the sum of its label and the labels of its two endpoints, determine a proper edge coloring of the graph. We propose two integer programming formulations and derive valid inequalities which are added as cutting planes on a branch-and-cut framework. In order to improve the efficiency of the algorithm, we also develop initial and primal heuristics. The algorithm is tested on random instances and the computational results show that it is very effective in comparison with CPLEX. It is displayed that it reduces both the CPU time (for solved instances) and the final percentage gap (for unsolved instances), and that it is capable of solving instances that are out of the reach of CPLEX.
MSC:
05C15 Coloring of graphs and hypergraphs
05C85 Graph algorithms (graph-theoretic aspects)
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C10 Integer programming
90B18 Communication networks in operations research
90B50 Management decision making, including multiple objectives
90C59 Approximation methods and heuristics in mathematical programming
90C30 Nonlinear programming
Software:
CALMA; CPLEX
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References:
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