Learning a Hidden Matching

Authors:
Noga Alon;Richard Beigel;Simon Kasif;Steven Rudich;Benny Sudakov
Affiliations:
-;-;-;-;-
Venue:
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Year:
2002

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Abstract

We consider the problem of learning a matching (i.e., a graph in which all vertices have degree 0 or 1) in a model where the only allowed operation is to query whether a set of vertices induces an edge. This is motivated by a problem that arises in molecular biology. In the deterministic nonadaptive setting, we prove a (\frac{1}{2} + 0(1))(_2^n ) upper bound and a nearly matching 0.32(_2^n ) lower bound for the minimum possible number of queries. In contrast, if we allow randomness then we obtain (by a randomized, nonadaptive algorithm) a much lower O(n log n) upper bound, which is best possible (even for randomized fully adaptive algorithms).