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An Approximation Algorithm for l∞-Fitting Robinson Structures to Distances

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 dR on X minimizing the l∞-error ||d − dR||∞ = maxx,y∈X {|d(x, y) − dR(x, y)|}. A distance dR 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 diagonal along any row or column. Robinsonian distances generalize ultrametrics, line distances and occur in the seriation problems and in classification.
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Submitted on : Friday, February 6, 2009 - 2:59:22 PM
Last modification on : Sunday, June 26, 2022 - 12:18:00 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:00:38 PM


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  • HAL Id : inria-00359296, version 1
  • ARXIV : 0902.1261



Victor Chepoi, Morgan Seston. An Approximation Algorithm for l∞-Fitting Robinson Structures to Distances. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.265-276. ⟨inria-00359296⟩



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