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On the approximability of numerical taxonomy (fitting distances by tree metrics)

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Agarwala, Richa, Bafna, Vineet, Farach, Martin, Paterson, Michael S. and Thorup, Mikkel (1997) On the approximability of numerical taxonomy (fitting distances by tree metrics). University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)

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Abstract

We consider the problem of fitting an n x n distance matrix D by a tree metric T. Let e be the distance to the closest tree metric under the L[infinity] norm, that is e=minT{||T-D||[infinity]}. First we present an O(n2) algorithm for finding a tree metric T such that ||T-D||[infinity] <= 3e. Second we show that it is NP-hard to find a tree metric T such that ||T-D||inf <= 9e/8. This paper presents the first algorithm for this problem with a performance guarantee.

Item Type: Report
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Trees (Graph theory), Numerical taxonomy
Series Name: Department of Computer Science research report
Publisher: University of Warwick. Department of Computer Science
Official Date: July 1997
Dates:
DateEvent
July 1997Completion
Number: Number 330
Number of Pages: 14
DOI: CS-RR-330
Institution: University of Warwick
Theses Department: Department of Computer Science
Status: Not Peer Reviewed
Publication Status: Unpublished
Publisher Statement: R.&nbsp;Ararwala, V.&nbsp;Bafna, M.&nbsp;Farach, B.&nbsp;Narayanan, M.&nbsp;Paterson and M.&nbsp;Thorup, M. &ldquo;On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)&rdquo;, <i>Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms</i>, ACM/SIAM, New York, NY, pp.&nbsp;365-372 (1996)
Funder: National Science Foundation (U.S.) (NSF), European Strategic Programme of Research and Development in Information Technology (ESPRIT)
Grant number: BIR-9412594 (NSF), CCR-9501942 (NSF), 20244 (ESPRIT)
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