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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2496
URN: urn:nbn:de:0030-drops-24968
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2496/
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Bshouty, Nader H. ; Mazzawi, Hanna

Optimal Query Complexity for Reconstructing Hypergraphs

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1001Bshouty.Nader.2496.pdf (0.3 MB)

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

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},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2496},
  URN =		{urn:nbn:de:0030-drops-24968},
  doi =		{10.4230/LIPIcs.STACS.2010.2496},
  annote =	{Keywords: Query complexity, hypergraphs}
}

Keywords: Query complexity, hypergraphs
Collection: 27th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2010
Date of publication: 09.03.2010

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