  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 $$ O(\frac{m\log n}{\log m}) $$
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
$O(poly(n^d/m))$ 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 $$ O(\frac{m\log \frac{n^d}{m}}{\log
m}). $$ additive queries.
  Using the information theoretic bound the above query complexities are tight.
