A branch-and-bound algorithm for the minimum cut linear arrangement problem

  • Authors:

  • Gintaras Palubeckis;Dalius Rubliauskas

  • Affiliations:

  • Multimedia Engineering Department, Kaunas University of Technology, Kaunas, Lithuania 51368;Multimedia Engineering Department, Kaunas University of Technology, Kaunas, Lithuania 51368

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2012

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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,驴,c n驴1 is minimized, where c i , i驴{1,驴,n驴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.