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
On the Power of Additive Combinatorial Search Model
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
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
Network verification via routing table queries
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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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 n^b 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(mlognlogm) additive queries. This solves the open problem in [S. Choi, J.H. Kim, Optimal query complexity bounds for finding graphs, in: STOC, 2008, pp. 749-758]. Choi and Kim's proof holds for m=(logn)^@a for a sufficiently large constant @a and uses the graph theory. We use the algebraic approach for the problem. Our proof is simple and holds for any m.