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### An Approximation Algorithm for l_infinity Fitting Robinson Structures to Distances

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### Abstract

In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set $X$ and a distance $d$ on $X$, find a Robinsonian distance $d_R$ on $X$ minimizing the $l_{\infty}$-error $||d-d_R||_{\infty}=\mbox{max}_{x,y\in X}\{ |d(x,y)-d_R(x,y)|\}.$ A distance $d_R$ on a finite set $X$ is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonalalong any row or column. Robinsonian distances generalize ultrametrics, line distances and occur in the seriation problems and in classification.

### BibTeX - Entry

@InProceedings{chepoi_et_al:LIPIcs:2009:1816,
author =	{Victor Chepoi and Morgan Seston},
title =	{{An Approximation Algorithm for l_infinity Fitting Robinson Structures to Distances}},
booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
pages =	{265--276},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-09-5},
ISSN =	{1868-8969},
year =	{2009},
volume =	{3},
editor =	{Susanne Albers and Jean-Yves Marion},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1816},
URN =		{urn:nbn:de:0030-drops-18167},
doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1816},
annote =	{Keywords: Robinsonian dissimilarity, Approximation algorithm, Fitting problem}
}


 Keywords: Robinsonian dissimilarity, Approximation algorithm, Fitting problem Seminar: 26th International Symposium on Theoretical Aspects of Computer Science Related Scholarly Article: Issue date: 2009 Date of publication: 2009

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