Randomized Rounding for Routing and Covering Problems: Experiments and Improvements

  • Benjamin Doerr
  • Marvin Künnemann
  • Magnus Wahlström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6049)

Abstract

We investigate how the recently developed different approaches to generate randomized roundings satisfying disjoint cardinality constraints behave when used in two classical algorithmic problems, namely low-congestion routing in networks and max-coverage problems in hypergraphs. Based on our experiments, we also propose and investigate the following new ideas. For the low-congestion routing problems, we suggest to solve a second LP, which yields the same congestion, but aims at producing a solution that is easier to round. For the max-coverage instances, observing that the greedy heuristic also performs very good, we develop hybrid approaches, in the form of a strengthened method of derandomized rounding, and a simple greedy/rounding hybrid using greedy and LP-based rounding elements. Experiments show that these ideas significantly reduce the rounding errors.

For an important special case of max-coverage, namely unit disk max-domination, we also develop a PTAS. However, experiments show it less competitive than other approaches, except possibly for extremely high solution qualities.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Marvin Künnemann
    • 2
  • Magnus Wahlström
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Universität des SaarlandesSaarbrückenGermany

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