Combinatorial search
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
Reconstructing a Hamiltonian cycle by querying the graph: application to DNA physical mapping
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
An optimal procedure for gap closing in whole genome shotgun sequencing
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Gene Expression and Fast Construction of Distributed Evolutionary Representation
Evolutionary Computation
Linkage Problem, Distribution Estimation, and Bayesian Networks
Evolutionary Computation
Efficient Linkage Discovery by Limited Probing
Evolutionary Computation
The Journal of Machine Learning Research
Fda -a scalable evolutionary algorithm for the optimization of additively decomposed functions
Evolutionary Computation
Optimal query complexity bounds for finding graphs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Lower and upper bounds for linkage discovery
IEEE Transactions on Evolutionary Computation
Reconstructing weighted graphs with minimal query complexity
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Combinatorial search on graphs motivated by bioinformatics applications: a brief survey
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions
Journal of Computer and System Sciences
Network verification via routing table queries
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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We consider the problem of finding an unknown graph by using queries with an additive property. This problem was partially motivated by DNA shotgun sequencing and linkage discovery problems of artificial intelligence. Given a graph, an additive query asks the number of edges in a set of vertices while a cross-additive query asks the number of edges crossing between two disjoint sets of vertices. The queries ask the sum of weights for weighted graphs. For a graph G with n vertices and at most m edges, we prove that there exists an algorithm to find the edges of G using O(mlogn^2mlog(m+1)) queries of both types for all m. The bound is best possible up to a constant factor. For a weighted graph with a mild condition on weights, it is shown that O(mlognlogm) queries are enough provided m=(logn)^@a for a sufficiently large constant @a, which is best possible up to a constant factor if m=0. This settles, in particular, a conjecture of Grebinski [V. Grebinski, On the power of additive combinatorial search model, in: Proceedings of the 4th Annual International Conference on Computing and Combinatorics (COCOON 1998), Taipei, Taiwan, 1998, pp. 194-203] for finding an unweighted graph using additive queries. We also consider the problem of finding the Fourier coefficients of a certain class of pseudo-Boolean functions as well as a similar coin weighing problem.