On the hardness of approximating NP witnesses

Uriel Feige, Michael Langberg, Kobbi Nissim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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).

Original languageEnglish
Title of host publicationApproximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings
EditorsKlaus Jansen, Samir Khuller
PublisherSpringer Verlag
Number of pages12
ISBN (Electronic)9783540679967
StatePublished - 2000
Externally publishedYes
Event3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, Germany
Duration: 5 Sep 20008 Sep 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.


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