Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
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Given a set of objects O and a set of tests T, the abstract decision tree problem (DTP) is to construct a tree with minimum height that completely identifies the objects of O, by using the tests of T. No algorithm with a good approximation ratio is known to solve this problem. We give a theoretical support for this fact by showing that DTP does not admit an o(logn)-approximation algorithm unless P=NP.