Lower bounds for the bandwidth problem

F. Rendl, Renata Sotirov, Christian Truden

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The bandwidth problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel approaches to obtain lower bounds for the bandwidth problem. In particular, we use vertex partitions to bound the bandwidth of a graph. Our approach contains prior approaches for bounding the bandwidth as special cases. By varying sizes of partitions, we achieve a trade-off between quality of bounds and efficiency of computing them. To compute lower bounds, we derive a Semidefinite Programming relaxation. We evaluate the performance of our approach on several data sets, including real-world instances.
Original languageEnglish
Article number105422
JournalComputers & Operations Research
Volume135
DOIs
Publication statusPublished - Nov 2021

Keywords

  • Bandwidth Problem
  • Graph partition
  • Semidefinite programming

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