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Summary: Learning a Hidden Matching
Combinatorial Identification of Hidden Matchings with Applications to Whole Genome Sequencing
Noga Alon
Richard Beigel
Simon Kasif
Steven Rudich §
Benny Sudakov ¶
May 8, 2002
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 (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).
1 Introduction
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