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].#R##N##R##N#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.
['Nader H. Bshouty', 'Hanna Mazzawi']
Reconstructing weighted graphs with minimal query complexity