Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Banerjee, Indranil; Richards, Dana https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-60448
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Sorting Under Forbidden Comparisons

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Abstract

In this paper we study the problem of sorting under forbidden comparisons where some pairs of elements may not be compared (forbidden pairs). Along with the set of elements V the input to our problem is a graph G(V, E), whose edges represents the pairs that we can compare in constant time. Given a graph with n vertices and m = binom(n)(2) - q edges we propose the first non-trivial deterministic algorithm which makes O((q + n)*log(n)) comparisons with a total complexity of O(n^2 + q^(omega/2)), where omega is the exponent in the complexity of matrix multiplication. We also propose a simple randomized algorithm for the problem which makes widetilde O(n^2/sqrt(q+n) + nsqrt(q)) probes with high probability. When the input graph is random we show that widetilde O(min(n^(3/2), pn^2)) probes suffice, where p is the edge probability.

BibTeX - Entry

@InProceedings{banerjee_et_al:LIPIcs:2016:6044,
  author =	{Indranil Banerjee and Dana Richards},
  title =	{{Sorting Under Forbidden Comparisons}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6044},
  URN =		{urn:nbn:de:0030-drops-60448},
  doi =		{10.4230/LIPIcs.SWAT.2016.22},
  annote =	{Keywords: Sorting, Random Graphs, Complexity}
}

Keywords: Sorting, Random Graphs, Complexity
Seminar: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue date: 2016
Date of publication: 22.06.2016


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