An Improved Approximation Algorithm for Knapsack Median Using Sparsification

  • Jaroslaw Byrka
  • Thomas Pensyl
  • Bartosz Rybicki
  • Joachim Spoerhase
  • Aravind Srinivasan
  • Khoa Trinh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)

Abstract

Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known algorithms in several ways, including adding randomization and applying sparsification as a preprocessing step. The latter improvement produces the first LP for this problem with bounded integrality gap. The new algorithm obtains an approximation factor of 17.46. We also give a 3.05 approximation with small budget violation.

Keywords

approximation algorithm combinatorial optimization randomized algorithm facility-location problems 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jaroslaw Byrka
    • 1
  • Thomas Pensyl
    • 2
  • Bartosz Rybicki
    • 1
  • Joachim Spoerhase
    • 1
  • Aravind Srinivasan
    • 3
  • Khoa Trinh
    • 2
  1. 1.Institute of Computer ScienceUniversity of WroclawWrocławPoland
  2. 2.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  3. 3.Department of Computer Science and Instute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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