Abstract
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(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)α for a sufficiently large constant α and uses the graph theory. We use the algebraic approach for the problem. Our proof is simple and holds for any m.
Published Version
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