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Article: Approximating the minimum triangulation of convex 3-polytopes with bounded degrees
Title | Approximating the minimum triangulation of convex 3-polytopes with bounded degrees |
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Authors | |
Keywords | Approximation algorithms Convex 3-polytopes Minimum triangulation |
Issue Date | 2005 |
Publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/comgeo |
Citation | Computational Geometry: Theory And Applications, 2005, v. 32 n. 1, p. 1-12 How to Cite? |
Abstract | Finding minimum triangulations of convex 3-polytopes is NP-hard. The best approximation algorithms only give an approximation ratio of 2 for this problem, which is the best possible asymptotically when only combinatorial structures of the polytopes are considered. In this paper we improve the approximation ratio of finding minimum triangulations for some special classes of 3-dimensional convex polytopes. (1) For polytopes without 3-cycles and degree-4 vertices we achieve a tight approximation ratio of 3/2. (2) For polytopes where all vertices have degrees at least 5, we achieve an upper bound of 2-112 on the approximation ratio. (3) For polytopes with n vertices and vertex degrees bounded above by Δ we achieve an asymptotic tight ratio of 2-Ω(1/Δ)-Ω(Δ/n). When Δ is constant the ratio can be shown to be at most 2-2/(Δ+1). © 2005 Elsevier B.V. All rights reserved. |
Persistent Identifier | http://hdl.handle.net/10722/89093 |
ISSN | 2023 Impact Factor: 0.4 2023 SCImago Journal Rankings: 0.497 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Fung, SPY | en_HK |
dc.contributor.author | Chin, FYL | en_HK |
dc.contributor.author | Poon, CK | en_HK |
dc.date.accessioned | 2010-09-06T09:52:18Z | - |
dc.date.available | 2010-09-06T09:52:18Z | - |
dc.date.issued | 2005 | en_HK |
dc.identifier.citation | Computational Geometry: Theory And Applications, 2005, v. 32 n. 1, p. 1-12 | en_HK |
dc.identifier.issn | 0925-7721 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/89093 | - |
dc.description.abstract | Finding minimum triangulations of convex 3-polytopes is NP-hard. The best approximation algorithms only give an approximation ratio of 2 for this problem, which is the best possible asymptotically when only combinatorial structures of the polytopes are considered. In this paper we improve the approximation ratio of finding minimum triangulations for some special classes of 3-dimensional convex polytopes. (1) For polytopes without 3-cycles and degree-4 vertices we achieve a tight approximation ratio of 3/2. (2) For polytopes where all vertices have degrees at least 5, we achieve an upper bound of 2-112 on the approximation ratio. (3) For polytopes with n vertices and vertex degrees bounded above by Δ we achieve an asymptotic tight ratio of 2-Ω(1/Δ)-Ω(Δ/n). When Δ is constant the ratio can be shown to be at most 2-2/(Δ+1). © 2005 Elsevier B.V. All rights reserved. | en_HK |
dc.language | eng | en_HK |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/comgeo | en_HK |
dc.relation.ispartof | Computational Geometry: Theory and Applications | en_HK |
dc.rights | Computational Geometry. Copyright © Elsevier BV. | en_HK |
dc.subject | Approximation algorithms | en_HK |
dc.subject | Convex 3-polytopes | en_HK |
dc.subject | Minimum triangulation | en_HK |
dc.title | Approximating the minimum triangulation of convex 3-polytopes with bounded degrees | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0925-7721&volume=32&issue=1&spage=1&epage=12&date=2005&atitle=Approximating+the+minimum+triangulation+of+convex+3-polytopes+with+bounded+degrees | en_HK |
dc.identifier.email | Chin, FYL:chin@cs.hku.hk | en_HK |
dc.identifier.authority | Chin, FYL=rp00105 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.comgeo.2005.03.001 | en_HK |
dc.identifier.scopus | eid_2-s2.0-22544484811 | en_HK |
dc.identifier.hkuros | 102714 | en_HK |
dc.identifier.volume | 32 | en_HK |
dc.identifier.issue | 1 | en_HK |
dc.identifier.spage | 1 | en_HK |
dc.identifier.epage | 12 | en_HK |
dc.identifier.isi | WOS:000230985700001 | - |
dc.publisher.place | Netherlands | en_HK |
dc.identifier.scopusauthorid | Fung, SPY=7201970079 | en_HK |
dc.identifier.scopusauthorid | Chin, FYL=7005101915 | en_HK |
dc.identifier.scopusauthorid | Poon, CK=7202673523 | en_HK |
dc.identifier.issnl | 0925-7721 | - |