A New Measure for the Bandwidth Minimization Problem

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The Bandwidth Minimization Problem for Graphs (BMPG) can be defined as finding a labeling for the vertices of a graph, where the maximum absolute difference between labels of each pair of connected vertices is minimum. The most used measure for the BMPG algorithms isβ, that indicates only the maximum of all absolute differences.

After analyzing some drawbacks of β, a measure, calledγ, which uses a positional numerical system with variable base and takes into account all the absolute differences of a graph is given.

In order to test the performance of γ and β a stochastic search procedure based on a Simulated Annealing (SA) algorithm has been applied to solve the BMPG. The experiments show that the SA that uses γ has better results for many classes of graphs than the one that uses β.