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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 (1999) On the approximability of numerical taxonomy (fitting distances by tree metrics). SIAM Journal on Computing, Volume 28 (Number 3). pp. 1073-1085. ISSN 0097-5397.
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Official URL: http://dx.doi.org/10.1137/S0097539795296334
Abstract
We consider the problem of fitting an n x n distance matrix D by a tree metric T. Let epsilon be the distance to the closest tree metric under the L-infinity norm; that is, epsilon = min(T) {parallel to T ? D parallel to infinity}. First we present an O(n(2)) algorithm for finding a tree metric T such that parallel to T ? D parallel to infinity less than or equal to 3 epsilon. Second we show that it is NP-hard to find a tree metric T such that parallel to T ? D parallel to infinity < 9/8 epsilon. This paper presents the first algorithm for this problem with a performance guarantee.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QA Mathematics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Journal or Publication Title: | SIAM Journal on Computing | ||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||
| ISSN: | 0097-5397 | ||||
| Official Date: | 1999 | ||||
| Dates: |
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| Volume: | Volume 28 | ||||
| Number: | Number 3 | ||||
| Number of Pages: | 13 | ||||
| Page Range: | pp. 1073-1085 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published |
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