Learning a Hidden Matching

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 (1 2 + o(1)) n 2 upper bound and a nearly matching 0.32 n 2 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).

• Type: Conference
• Year: 2002
• Where: FOCS
• Authors: Noga Alon, Richard Beigel, Simon Kasif, Steven Rudich, Benny Sudakov
• Keywords: Allowed Operation, Deterministic Nonadaptive Setting, FOCS 2002, Theoretical Computer Science, Upper Bound