Reconstructing weighted graphs with minimal query complexity

Abstract: In this paper, we consider the problem of reconstructing a hidden weighted graph using additive queries. We prove the following. Let be a weighted hidden graph with  vertices and edges such that the weights on the edges are bounded between  and  for any positive constants  and . For any , there exists a non-adaptive algorithm that finds the edges of the graph using 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 for a sufficiently large constant  and uses the graph theory. We use the algebraic approach for the problem. Our proof is simple and holds for any . [Copyright &y& Elsevier]