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On bounded queries and approximation

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2 Author(s)
Chang, R. ; Dept. of Comput. Sci., Maryland Univ., Baltimore, MD, USA ; Gasarch, W.I.

This paper investigates the computational complexity of approximating NP-optimization problems using the number of queries to an NP oracle as a complexity measure. The results show a trade-off between the closeness of the approximation and the number of queries required. For an approximation factor k(n), loglogk(n) n queries to an NP oracle can be used to approximate the maximum clique size of a graph within a factor of k(n). However, this approximation cannot be achieved using fewer than loglogk(n) n-c queries to any oracle unless P=NP, where c is a constant that does not depend on k. These results hold when k(n) belongs to a class of functions which include any integer constant function, log n, loga n and n1a/. Similar results are obtained for graph coloring, set cover and other NP-optimization problems

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993