The Journal of Machine Learning Research
Optimal query complexity bounds for finding graphs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Learning and Verifying Graphs Using Queries with a Focus on Edge Counting
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Nonadaptive algorithms for threshold group testing
Discrete Applied Mathematics
Optimal query complexity bounds for finding graphs
Artificial Intelligence
Finding maximum degrees in hidden bipartite graphs
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Reconstructing weighted graphs with minimal query complexity
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Optimally reconstructing weighted graphs using queries
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Toward a deterministic polynomial time algorithm with optimal additive query complexity
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Inferring social networks from outbreaks
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions
Journal of Computer and System Sciences
Reconstruction of hidden graphs and threshold group testing
Journal of Combinatorial Optimization
Exact and approximate algorithms for the most connected vertex problem
ACM Transactions on Database Systems (TODS)
Group testing with multiple mutually-obscuring positives
Information Theory, Combinatorics, and Search Theory
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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}+o(1)){n \choose 2} $ upper bound and a nearly matching $0.32{n \choose 2}$ 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).