TY - JOUR

T1 - Learning a hidden matching

AU - Alon, Noga

AU - Beigel, Richard

AU - Kasif, Simon

AU - Rudich, Steven

AU - Sudakovh, Benny

PY - 2004/1

Y1 - 2004/1

N2 - 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).

AB - 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).

KW - Combinatorial search problems

KW - Finite protective planes

KW - Genome sequencing

KW - Matchings in graphs

UR - http://www.scopus.com/inward/record.url?scp=2342650135&partnerID=8YFLogxK

U2 - 10.1137/S0097539702420139

DO - 10.1137/S0097539702420139

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AN - SCOPUS:2342650135

SN - 0097-5397

VL - 33

SP - 487

EP - 501

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 2

ER -