An optimal procedure for gap closing in whole genome shotgun sequencing
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Machine Learning
Machine Learning
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Optimal Query Bounds for Reconstructing a Hamiltonian Cycle in Complete Graphs
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
The Journal of Machine Learning Research
Competitive group testing and learning hidden vertex covers with minimum adaptivity
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Finding maximum degrees in hidden bipartite graphs
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Inferring social networks from outbreaks
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
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)
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We consider the problem of learning a general graph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden graph. This model has been studied for particular classes of graphs by Grebinski and Kucherov [V. Grebinski, G. Kucherov, Optimal query bounds for reconstructing a Hamiltonian cycle in complete graphs, in: Fifth Israel Symposium on the Theory of Computing Systems, 1997, pp. 166-173] and Alon et al. [N. Alon, R. Beigel, S. Kasif, S. Rudich, B. Sudakov, Learning a hidden matching, in: The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002, pp. 197-206], motivated by problems arising in genome sequencing. We give an adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(mlogn) queries, which is tight up to a constant factor for classes of non-dense graphs. Allowing randomness, we give a 5-round Las Vegas algorithm using O(mlogn+mlog^2n) queries in expectation. We give a lower bound of @W((2m/r)^r^/^2) for learning the class of non-uniform hypergraphs of dimension r with m edges.