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Approximation Hardness for Small Occurrence Instances of NP-Hard Problems

  • Miroslav Chlebík
  • Janka Chlebíková
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2653)

Abstract

The paper contributes to the systematic study (started by Berman and Karpinski) of explicit approximability lower bounds for small occurrence optimization problems.We present parametrized reductions for some packing and covering problems, including 3-Dimensional Matching, and prove the best known inapproximability results even for highly restricted versions of them. For example, we show that it is NP-hard to approximate Max-3-DM within \( \frac{{139}} {{138}} \) even on instances with exactly two occurrences of each element. Previous known hardness results for bounded occurence case of the problem required that the bound is at least three, and even then no explicit lower bound was known.

New structural results which improve the known bounds for 3-regular amplifiers and hence the inapproximability results for numerous small occurrence problems studied earlier by Berman and Karpinski are also presented.

Keywords

Hardness Result Steiner Tree Problem Contact Node Inapproximability Result Small Occurrence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Miroslav Chlebík
    • 1
  • Janka Chlebíková
    • 2
  1. 1.MPI for Mathematics in the SciencesLeipzig
  2. 2.Institut für Informatik und Praktische MathematikCAUKiel

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