License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1816
URN: urn:nbn:de:0030-drops-18167
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/1816/
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Chepoi, Victor ; Seston, Morgan

An Approximation Algorithm for l_infinity Fitting Robinson Structures to Distances

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09001.ChepoiV.1816.pdf (0.2 MB)

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 =		{10.4230/LIPIcs.STACS.2009.1816},
  annote =	{Keywords: Robinsonian dissimilarity, Approximation algorithm, Fitting problem}
}

Keywords: Robinsonian dissimilarity, Approximation algorithm, Fitting problem
Collection: 26th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2009
Date of publication: 19.02.2009

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