More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP

Lars Engebretsen; Jonas Holmerin

doi:10.1002/rsa.20226

More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP

Random Structures and Algorithms ◽

10.1002/rsa.20226 ◽

2008 ◽

Vol 33 (4) ◽

pp. 497-514 ◽

Cited By ~ 6

Author(s):

Lars Engebretsen ◽

Jonas Holmerin

Keyword(s):

Approximation Hardness

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Approximation Hardness of the Cross-Species Conserved Active Modules Detection Problem

Lecture Notes in Computer Science - SOFSEM 2015: Theory and Practice of Computer Science ◽

10.1007/978-3-662-46078-8_20 ◽

2015 ◽

pp. 242-253

Author(s):

Thomas Hume ◽

Hayssam Soueidan ◽

Macha Nikolski ◽

Guillaume Blin

Keyword(s):

Detection Problem ◽

Approximation Hardness ◽

The Cross

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Corrigendum to “Approximation hardness of min–max tree covers” [Oper. Res. Lett. 38 (3) (2010) 169–173]

Operations Research Letters ◽

10.1016/j.orl.2013.07.002 ◽

2013 ◽

Vol 41 (5) ◽

pp. 563

Author(s):

Zhou Xu ◽

Qi Wen

Keyword(s):

Approximation Hardness

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On the approximation hardness of dense TSP and other path problems

Information Processing Letters ◽

10.1016/s0020-0190(99)00048-4 ◽

1999 ◽

Vol 70 (2) ◽

pp. 53-55 ◽

Cited By ~ 3

Author(s):

W. Fernandez de la Vega ◽

M. Karpinski

Keyword(s):

Approximation Hardness

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On the Hardness of Approximating Some Optimization Problems That Are Supposedly Easier Than MAX CLIQUE

Combinatorics Probability Computing ◽

10.1017/s0963548300001553 ◽

1995 ◽

Vol 4 (2) ◽

pp. 167-180 ◽

Cited By ~ 1

Author(s):

Oleg Verbitsky

Keyword(s):

Polynomial Time ◽

Optimization Problems ◽

Constant Factor ◽

Interactive Proof ◽

Complete Problem ◽

Np Optimization ◽

Approximation Hardness ◽

Recent Developments ◽

Proof Techniques

We focus our attention on the class RMAX(2) of NP optimization problems. Owing to recent developments in interactive proof techniques, RMAX(2) was shown to be the lowest class of logical classification that contains problems hard to approximate. Namely, the RMAX(2)-complete problem MAX CLIQUE (of finding the size of the largest clique in a graph) is not approximable in polynomial time within any constant factor unless NP=P.We are interested in problems inside RMAX(2) that are not known to be complete but are still hard to approximate. We point out that one such problem is MAXlog n, n, considered by Berman and Schnitger: given m conjunctions, each of them consisting of log m propositional variables or their negations, find the maximal number of simultaneously satisfiable conjunctions. We also obtain the approximation hardness results for some other problems in RMAX(2). Finally, we discuss the question of whether or not the problems under consideration are RMAX(2)-complete.

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