Integrality gaps for colorful matchings

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Abstract

We study the integrality gap of the natural linear programming relaxation for the Bounded Color Matching (BCM) problem. We provide several families of instances and establish lower bounds on their integrality gaps and we study how the Sherali-Adams "lift-and-project" technique behaves on these instances. We complement these results by showing that if we exclude certain simple sub-structures from our input graphs, then the integrality gap of the natural linear formulation strictly improves. To prove this, we adapt for our purposes the results of Furedi (1981). We further leverage this to show upper bounds on the performance of the Sherali-Adams hierarchy when applied to the natural LP relaxation of the BCM problem. (C) 2018 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)73-92
Number of pages20
JournalDiscrete Optimization
Volume32
Early online date12 Jan 2019
DOIs
Publication statusPublished - May 2019

Keywords

  • APPROXIMATION ALGORITHMS
  • COMPLEXITY
  • Colorful matchings
  • Integrality gap
  • LIFT
  • Lift and project
  • Linear programming
  • RELAXATIONS
  • SEMIDEFINITE
  • SET
  • SHERALI-ADAMS
  • Sherali-Adams
  • TRANSVERSAL
  • WEIGHT

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