When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2496
URN: urn:nbn:de:0030-drops-24968
URL: https://drops.dagstuhl.de/opus/volltexte/2010/2496/
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### Optimal Query Complexity for Reconstructing Hypergraphs

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### 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
$$O\left(\frac{m\log n}{\log m}\right)$$
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
$$O\left(\frac{m\log \frac{n^d}{m}}{\log m}\right).$$

Using the information theoretic bound the above query complexities
are tight.

### BibTeX - Entry

@InProceedings{bshouty_et_al:LIPIcs:2010:2496,
author =	{Nader H. Bshouty and Hanna Mazzawi},
title =	{{Optimal Query Complexity for Reconstructing Hypergraphs}},
booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
pages =	{143--154},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-16-3},
ISSN =	{1868-8969},
year =	{2010},
volume =	{5},
editor =	{Jean-Yves Marion and Thomas Schwentick},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},