 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.SWAT.2016.22
URN: urn:nbn:de:0030-drops-60448
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6044/
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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},
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