How well can primal-dual and local-ratio algorithms perform?

  • Authors:
  • Allan Borodin;David Cashman;Avner Magen

  • Affiliations:
  • Department of Computer Science, University of Toronto;Department of Computer Science, University of Toronto;Department of Computer Science, University of Toronto

  • Venue:
  • ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
  • Year:
  • 2005

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Abstract

We define an algorithmic paradigm, the stack model, that captures most primal-dual and local-ratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations. Hence our approximation bounds are independent of the P vs NP question. We provide tools to bound the performance of primal dual and local ratio algorithms and supply a (log n+1)/2 inapproximability result for set-cover, a 4/3 inapproximability for min steiner tree, and a 0.913 inapproximability for interval scheduling on two machines.