Optimal Query Complexity for Reconstructing Hypergraphs

Nader H. Bshouty & Hanna Mazzawi
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 $$ O\left(\frac{m\log n}{\log m}\right) $$ additive queries. This solves the open problem in [S. Choi, J. H. Kim....