文章基本信息

标题：On Syntactic versus Computational views of Approximability
本地全文：下载
作者：Sanjeev Khanna ; Rajeev Motwani ; Madhu Sudan 等
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1995
卷号：1995
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We attempt to reconcile the two distinct views of approximation classes: syntactic and computational. Syntactic classes such as MAX SNP allow for clean complexity-theoretic results and natural complete problems, while computational classes such as APX allow us to work with problems whose approximability is well-understood. Our results give a computational framework for studying syntactic classes, and provide a syntactic characterization of computational classes, as follows. We compare the syntactically defined class MAX SNP with the computationally defined class APX and show that every problem in APX can be ``placed'' (i.e., L-reduced to a problem) in MAX SNP. Our methods introduce a general techique for creating approximation preserving reductions which show that any ``well'' approximable problem can be reduced (in an approximation preserving manner) to a problem which is hard to approximate to corresponding factors. We demonstrate this technique by applying it to the classes RMAX(2) and MIN F^+ \Pi_2$ which have the Set Cover problem and the Clique problem as complete problems, respectively. We use the syntactic nature of MAX SNP to define a general paradigm, non-oblivious local search, useful for developing simple yet efficient approximation algorithms. We show that such algorithms can find good approximations for all MAX SNP problems, yielding approximation ratios comparable to the best-known for a variety of specific MAX SNP-complete problems. Non-oblivious local search provably out-performs standard local search in both the degree of approximation achieved, and the efficiency of the resulting algorithms.
关键词：Approximation Algorithms, complete problems, computational classes, computationalcomplexity, polynomial reducibilities