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computational complexity

, Volume 4, Issue 2, pp 133–157 | Cite as

The hardness of approximation: Gap location

  • Erez Petrank
Article

Abstract

We refine the complexity analysis of approximation problems by relating it to a new parameter calledgap location. Many of the results obtained so far for approximations yield satisfactory analysis with respect to this refined parameter, but some known results (e.g.,max-k-colorability, max 3-dimensional matching andmax not-all-equal 3sat) fall short of doing so. As a second contribution, our work fills the gap in these cases by presenting new reductions.

Next, we present definitions and hardness results of new approximation versions of some NP-complete optimization problems. The problems we treat arevertex cover (for which we define a different optimization problem from the one treated in Papadimitriou & Yannakakis 1991),k-edge coloring, andset splitting.

Key words

Hardness of approximation approximation algorithms computational complexity NP-hardness 

Subject classifications

03D15 68Q25 68Q15 68R10 

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Erez Petrank
    • 1
  1. 1.Department of Computer ScienceTechnion - Israel Institute of TechnologyTechnion city HaifaIsrael

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