Abstract
Given an edge-weighted graph G of order n, the minimum cut linear arrangement problem (MCLAP) asks to find a one-to-one map from the vertices of G to integers from 1 to n such that the largest of the cut values c 1,…,c n−1 is minimized, where c i , i∈{1,…,n−1}, is the total weight of the edges connecting vertices mapped to integers 1 through i with vertices mapped to integers i+1 through n. In this paper, we present a branch-and-bound algorithm for solving this problem. A salient feature of the algorithm is that it employs a dominance test which allows reducing the redundancy in the enumeration process drastically. The test is based on the use of a tabu search procedure developed to solve the MCLAP. We report computational results for both the unweighted and weighted graphs. In particular, we focus on calculating the cutwidth of some well-known graphs from the literature.
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Palubeckis, G., Rubliauskas, D. A branch-and-bound algorithm for the minimum cut linear arrangement problem. J Comb Optim 24, 540–563 (2012). https://doi.org/10.1007/s10878-011-9406-2
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DOI: https://doi.org/10.1007/s10878-011-9406-2