The Inapproximability of Non NP-hard Optimization Problems
نویسندگان
چکیده
The inapproximability of non NP-hard optimization problems is investigated. Techniques are given to show that problems Log Dominating Set and Log Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems and a PCP characterization of NP. Reductions from the PCP characterization show that Log Clique is not approximable in polynomial time and Max Sparse SAT does not have a PTAS under the assumption that SAT cannot be solved in deterministic 2 O(logn p n) time and that NP 6 6 DTIME(2 o(n)). A number of non-trivial approximation-preserving reductions are also presented, making it possible to extend inapproximability results to more natural non NP-hard problems such as Tournament Dominating Set and Rich Hypergraph Vertex Cover.
منابع مشابه
Notes on the PCP Theorem and Complexity of Approximations
We know that a number of important optimization problems are NP-hard to solve exactly. Today we begin the study of the complexity of finding approximate solutions. There is a fundamental difficulty in proving hardness of approximation results. All the NPcompleteness proofs for graph problems before 1990 can be essentially described as follows: we start from the computation of a generic non-dete...
متن کاملLecture 1: Approximation Algorithms, Approximation Ratios, Gap Problems
To date, thousands of natural optimization problems have been shown to be NP-hard [6, 13]. Designing approximation algorithms [4, 17, 21] has become a standard path to attack these problems. For some problem, however, it is even NP-hard to approximate the optimal solution to within a certain ratio. The TRAVELING SALESMAN PROBLEM (TSP), for instance, has no approximation algorithm, since finding...
متن کاملParallelizing Assignment Problem with DNA Strands
Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...
متن کاملInapproximability Reductions and Integrality Gaps
In this thesis we prove intractability results for several well studied problems in combinatorial optimization. Closest Vector Problem with Pre-processing (CVPP): We show that the pre-processing version of the well known Closest Vector Problem is hard to approximate to an almost polynomial factor (2 1− ) unless NP is in quasi polynomial time. The approximability of CVPP is closely related to th...
متن کاملLec . 1 : Approximation Algorithms for NP - hard problems
In this course, we will be studying, as the title suggests, the approximability and inapproximability (limits of approximability) of different combinatorial optimization problems. All the problems we will be looking at will be ones that lack efficient algorithms and in particular will be NP-hard problems. The last two-three decades has seen remarkable progress in approximation algorithms for se...
متن کامل