Combinatorial search
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
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
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
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
Optimal query complexity bounds for finding graphs
Artificial Intelligence
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
On parity check (0, 1)-matrix over Zp
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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In this paper we consider the problem of reconstructing a hidden weighted graph using additive queries. We prove the following: Let G be a weighted hidden graph with n vertices and m edges such that the weights on the edges are bounded between n-a and nb for any positive constants a and b. For any m there exists a non-adaptive algorithm that finds the edges of the graph using O (mlog n/log m) additive queries. This solves the open problem in [S. Choi, J. H. Kim. Optimal Query Complexity Bounds for Finding Graphs. Proc. of the 40th annual ACM Symposium on Theory of Computing , 749-758, 2008]. Choi and Kim's proof holds for m ≥ (log n)α for a sufficiently large constant α and uses graph theory. We use the algebraic approach for the problem. Our proof is simple and holds for any m.