Randomized rounding for routing and covering problems: experiments and improvements

  • Authors:

  • Benjamin Doerr;Marvin Künnemann;Magnus Wahlström

  • Affiliations:

  • Max-Planck-Institut für Informatik, Saarbrücken, Germany;Universität des Saarlandes, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany

  • Venue:
  • SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
  • Year:
  • 2010

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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.