Non deterministic polynomial optimization problems and their approximations
Azaria Paz,Shlomo Moran +1 more
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TLDR
A unified and general framework for the study of nondeterministic polynomial optimization problems (NPOP) is presented and some properties of NPOP's are investigated.About:
This article is published in Theoretical Computer Science.The article was published on 1981-01-01 and is currently open access. It has received 174 citations till now. The article focuses on the topics: Optimization problem & NP.read more
Citations
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Journal ArticleDOI
A threshold of ln n for approximating set cover
TL;DR: It is proved that (1 - o(1) ln n setcover is a threshold below which setcover cannot be approximated efficiently, unless NP has slightlysuperpolynomial time algorithms.
Journal ArticleDOI
Optimization, approximation, and complexity classes
TL;DR: It follows that such a complete problem has a polynomial-time approximation scheme iff the whole class does, and that a number of common optimization problems are complete for MAX SNP under a kind of careful transformation that preserves approximability.
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Proof verification and the hardness of approximation problems
TL;DR: It is proved that no MAX SNP-hard problem has a polynomial time approximation scheme, unless NP = P, and there exists a positive ε such that approximating the maximum clique size in an N-vertex graph to within a factor of Nε is NP-hard.
Proceedings ArticleDOI
Proof verification and hardness of approximation problems
TL;DR: Agarwal et al. as discussed by the authors showed that the MAXSNP-hard problem does not have polynomial-time approximation schemes unless P=NP, and for some epsilon > 0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup 1/ε / unless P = NP.
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On the hardness of approximating minimization problems
Carsten Lund,Mihalis Yannakakis +1 more
TL;DR: It is proved that there is an e > 0 such that Graph Coloring cannot be approximated with ratio n e unless P = NP, and Set Covering cannot be approximation with ratio c log n for any c < 1/4 unless NP is contained in DTIME(n poly log n).
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
P-Complete Approximation Problems
Sartaj Sahni,Teofilo F. Gonzalez +1 more
TL;DR: For P- complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete.
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Relationships between nondeterministic and deterministic tape complexities
TL;DR: The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.