On the Hardness of Approximating NP Witnesses

  • Uriel Feige
  • Michael Langberg
  • Kobbi Nissim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1913)

Abstract

The search version for NP-complete combinatorial optimization problems asks for finding a solution of optimal value. Such a solution is called a witness. We follow a recent paper by Kumar and Sivakumar, and study a relatively new notion of approximate solutions that ignores the value of a solution and instead considers its syntactic representation (under some standard encoding scheme). The results that we present are of a negative nature. We show that for many of the well known NP-complete problems (such as 3-SAT, CLIQUE, 3-COLORING, SET COVER) it is NP-hard to produce a solution whose Hamming distance from an optimal solution is substantially closer than what one would obtain by just taking a random solution. In fact, we have been able to show similar results for most of Karp’s 21 original NP-complete problems. (At the moment, our results are not tight only for UNDIRECTED HAMILTONIAN CYCLE and FEEDBACK EDGE SET.)

Keywords

HAMILTONIAN Cycle Vertex Cover Maximum Clique Hardness Result Satisfying Assignment 
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 2000

Authors and Affiliations

  • Uriel Feige
    • 1
  • Michael Langberg
    • 1
  • Kobbi Nissim
    • 1
  1. 1.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovot

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