On Bounded Queries and Approximation

This paper investigates the computational complexity of approximating several NPoptimization 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), log logk(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 log logk(n) n − c queries to any oracle unless P = NP, where c is a constant that does not depend on k. These results hold for approximation factors k(n) ≥ 2 that belong to a class of functions which includes any integer constant function, log n, loga n and n1/a. Similar results are obtained for graph coloring, set cover and other NP-optimization problems. ∗ Supported in part by NSF Research Grant CCR-9309137. † Supported in part by NSF Research Grant CCR-9020079. 

• Type: Conference
• Year: 1993
• Where: FOCS
• Authors: Richard Chang, William I. Gasarch
• Keywords: Approximation, Approximation Factors, FOCS 1993, NP Oracle, Theoretical Computer Science