License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.3
URN: urn:nbn:de:0030-drops-95854
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9585/
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Abasi, Hasan

Error-Tolerant Non-Adaptive Learning of a Hidden Hypergraph

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LIPIcs-MFCS-2018-3.pdf (0.5 MB)

Abstract

We consider the problem of learning the hypergraph using edge-detecting queries. In this model, the learner is allowed to query whether a set of vertices includes an edge from a hidden hypergraph. Except a few, all previous algorithms assume that a query's result is always correct. In this paper we study the problem of learning a hypergraph where alpha -fraction of the queries are incorrect. The main contribution of this paper is generalizing the well-known structure CFF (Cover Free Family) to be Dense (we will call it DCFF - Dense Cover Free Family) while presenting three different constructions for DCFF. Later, we use these constructions wisely to give a polynomial time non-adaptive learning algorithm for a hypergraph problem with at most alpha-fracion incorrect queries. The hypergraph problem is also known as both monotone DNF learning problem, and complexes group testing problem.

BibTeX - Entry

@InProceedings{abasi:LIPIcs:2018:9585,
  author =	{Hasan Abasi},
  title =	{{Error-Tolerant Non-Adaptive Learning of a Hidden Hypergraph}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9585},
  URN =		{urn:nbn:de:0030-drops-95854},
  doi =		{10.4230/LIPIcs.MFCS.2018.3},
  annote =	{Keywords: Error Tolerant Algorithm, Hidden Hypergraph, Montone DNF, Group Testing, Non-Adaptive Learning}
}

Keywords: Error Tolerant Algorithm, Hidden Hypergraph, Montone DNF, Group Testing, Non-Adaptive Learning
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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