期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2010
卷号：2010
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple semidefinite programming and a rounding scheme for it.
In this paper, we show that a similar result holds for constant-time approximation algorithms in the bounded-degree model.
Specifically, we present the followings: (i) For every CSP, we construct an oracle that serves an access, in constant time, to a nearly optimal solution of a basic LP relaxation of the CSP. (ii) Using the oracle, we present a constant-time rounding scheme that achieves an approximation ratio oincident with the integrality gap of the basic LP.
(iii) We give a generic conversion from integrality gaps of basic LPs to hardness results.
All of those results are ``unconditional.'' Therefore, for every bounded-degree CSP, we give the best constant-time approximation algorithm among all.
关键词：constant-time approximation, Constraint satisfaction problems, linear programmings, rounding schemes
