On fixed-parameter tractability and approximability of NP-hard optimization problems

[1993] The 2nd Israel Symposium on Theory and Computing Systems Pub Date : 1993-06-07 DOI:10.1109/ISTCS.1993.253478

L. Cai, Jianer Chen

引用次数: 116

Abstract

Fixed-parameter tractability and approximability of NP-hard optimization problems are studied based on a model GC(s(n), Pi /sub k//sup L/). The main results are (1) a class of NP-hard optimization problems, including dominating-set and zero-one integer-programing, are fixed-parameter tractable if and only if GC(s(n), Pi /sub 2//sup L/) contained in P for some s(n) in omega (log n); (2) most approximable NP-hard optimization problems are fixed-parameter tractable. In particular, the class MAX NP is fixed-parameter tractable; (3) a class of optimization problems do not have fully polynomial time approximation scheme unless GC(s(n), Pi /sub k//sup L/) contained in P for some s(n) in omega (log n) and for some k>l; and (4) every fixed-parameter tractable optimization problem can be approximated in polynomial time to a non-trivial ratio.<>

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NP-hard优化问题的定参数可跟踪性和近似性

基于GC(s(n)， Pi /sub k//sup L/)模型，研究了NP-hard优化问题的定参数可跟踪性和近似性。主要结果是:(1)一类NP-hard优化问题，包括支配集和0 - 1整数规划，当且仅当对于(log n)中的某个s(n)， GC(s(n)， Pi /sub 2//sup L/)包含在P中是定参数可处理的;(2)大多数近似NP-hard优化问题是固定参数可处理的。特别地，MAX NP类是固定参数可处理的;(3)一类优化问题除非GC(s(n)， Pi /sub k//sup L/)包含在P中，对于(log n)中的某些s(n)和某些k> L，则不具有完全多项式时间逼近方案;(4)每一个固定参数可处理的优化问题都可以在多项式时间内逼近到一个非平凡的比率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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[1993] The 2nd Israel Symposium on Theory and Computing Systems

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