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- W1792906098 abstract "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 $$ O(frac{mlog n}{log m}) $$ 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 $$ O(frac{mlog frac{n^d}{m}}{log m}). $$ additive queries. Using the information theoretic bound the above query complexities are tight." @default.
- W1792906098 created "2016-06-24" @default.
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- W1792906098 date "2010-01-03" @default.
- W1792906098 modified "2023-09-25" @default.
- W1792906098 title "Optimal Query Complexity for Reconstructing Hypergraphs" @default.
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