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Optimal realization...
Optimal realizations of two-dimensional, totally-decomposable metrics
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- Herrmann, Sven (författare)
- Univ E Anglia, Sch Comp Sci, Norwich NR4 7TJ, Norfolk, England.
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- Koolen, Jack H. (författare)
- Univ Sci & Technol China, Sch Math Sci, Wen Tsun Wu Key Lab, CAS, Hefei, Peoples R China.
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- Lesser, Alice (författare)
- Uppsala universitet,Matematiska institutionen
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- Moulton, Vincent (författare)
- Univ E Anglia, Sch Comp Sci, Norwich NR4 7TJ, Norfolk, England.
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- Wu, Taoyang (författare)
- Univ E Anglia, Sch Comp Sci, Norwich NR4 7TJ, Norfolk, England.;Natl Univ Singapore, Dept Math, Singapore 119076, Singapore.
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Univ E Anglia, Sch Comp Sci, Norwich NR4 7TJ, Norfolk, England Univ Sci & Technol China, Sch Math Sci, Wen Tsun Wu Key Lab, CAS, Hefei, Peoples R China. (creator_code:org_t)
- Elsevier BV, 2015
- 2015
- Engelska.
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Ingår i: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 338:8, s. 1289-1299
- Relaterad länk:
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https://doi.org/10.1...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- A realization of a metric d on a finite set X is a weighted graph (G, w) whose vertex set contains X such that the shortest-path distance between elements of X considered as vertices in G is equal to d. Such a realization (G, w) is called optimal if the sum of its edge weights is minimal over all such realizations. Optimal realizations always exist, although it is NP-hard to compute them in general, and they have applications in areas such as phylogenetics, electrical networks and internet tomography. A. Dress (1984) showed that the optimal realizations of a metric dare closely related to a certain polytopal complex that can be canonically associated to d called its tight-span. Moreover, he conjectured that the (weighted) graph consisting of the zero- and one-dimensional faces of the tight-span of d must always contain an optimal realization as a homeomorphic subgraph. In this paper, we prove that this conjecture does indeed hold for a certain class of metrics, namely the class of totally-decomposable metrics whose tight-span has dimension two. As a corollary, it follows that the minimum Manhattan network problem is a special case of finding optimal realizations of two-dimensional totally-decomposable metrics. (C) 2015 Elsevier B.V. All rights reserved.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- Optimal realizations
- Totally-decomposable metrics
- Tight-span
- Manhattan network problem
- Buneman complex
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- ref (ämneskategori)
- art (ämneskategori)
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