In this paper we consider the problem of reconstructing a hidden weighted
hypergraph of constant rank using additive queries. We prove the following: Let
G be a weighted hidden hypergraph of constant rank with n vertices and m
hyperedges. For any m there exists a non-adaptive algorithm that finds the
edges of the graph and their weights using O(logmmlogn)
additive queries. This solves the open problem in [S. Choi, J. H. Kim. Optimal
Query Complexity Bounds for Finding Graphs. {\em STOC}, 749--758,~2008].
When the weights of the hypergraph are integers that are less than
O(poly(nd/m)) where d is the rank of the hypergraph (and therefore for
unweighted hypergraphs) there exists a non-adaptive algorithm that finds the
edges of the graph and their weights using O(logmmlogmnd). additive queries.
Using the information theoretic bound the above query complexities are tight