On the hardness of approximating NP witnesses

Uriel Feige; Michael Langberg; Kobbi Nissim

doi:10.1007/3-540-44436-x_13

On the hardness of approximating NP witnesses

Uriel Feige, Michael Langberg, Kobbi Nissim

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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).

Original language	English
Title of host publication	Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings
Editors	Klaus Jansen, Samir Khuller
Publisher	Springer Verlag
Pages	120-131
Number of pages	12
ISBN (Electronic)	9783540679967
DOIs	https://doi.org/10.1007/3-540-44436-x_13
State	Published - 2000
Externally published	Yes
Event	3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, Germany Duration: 5 Sep 2000 → 8 Sep 2000

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1913
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000
Country/Territory	Germany
City	Saarbrucken
Period	5/09/00 → 8/09/00

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

Access to Document

10.1007/3-540-44436-x_13

Cite this

Feige, U., Langberg, M., & Nissim, K. (2000). On the hardness of approximating NP witnesses. In K. Jansen, & S. Khuller (Eds.), Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings (pp. 120-131). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1913). Springer Verlag. https://doi.org/10.1007/3-540-44436-x_13

Feige, Uriel ; Langberg, Michael ; Nissim, Kobbi. / On the hardness of approximating NP witnesses. Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings. editor / Klaus Jansen ; Samir Khuller. Springer Verlag, 2000. pp. 120-131 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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{\textquoteright}s 21 original NP-complete problems. (At the moment, our results are not tight only for UNDIRECTED HAMILTONIAN CYCLE and FEEDBACK EDGE SET).",

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Feige, U, Langberg, M & Nissim, K 2000, On the hardness of approximating NP witnesses. in K Jansen & S Khuller (eds), Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1913, Springer Verlag, pp. 120-131, 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000, Saarbrucken, Germany, 5/09/00. https://doi.org/10.1007/3-540-44436-x_13

On the hardness of approximating NP witnesses. / Feige, Uriel; Langberg, Michael; Nissim, Kobbi.
Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings. ed. / Klaus Jansen; Samir Khuller. Springer Verlag, 2000. p. 120-131 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1913).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Feige U, Langberg M, Nissim K. On the hardness of approximating NP witnesses. In Jansen K, Khuller S, editors, Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings. Springer Verlag. 2000. p. 120-131. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44436-x_13

On the hardness of approximating NP witnesses

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