A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd
Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimiz...
Ausführliche Beschreibung
Autor*in: |
Van Laarhoven, Jon W. [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2010 |
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Schlagwörter: |
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Anmerkung: |
© Springer Science+Business Media, LLC 2010 |
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Übergeordnetes Werk: |
Enthalten in: Journal of heuristics - Springer US, 1995, 17(2010), 4 vom: 09. Juli, Seite 353-372 |
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Übergeordnetes Werk: |
volume:17 ; year:2010 ; number:4 ; day:09 ; month:07 ; pages:353-372 |
Links: |
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DOI / URN: |
10.1007/s10732-010-9137-z |
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Katalog-ID: |
OLC2039387587 |
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10.1007/s10732-010-9137-z doi (DE-627)OLC2039387587 (DE-He213)s10732-010-9137-z-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Van Laarhoven, Jon W. verfasserin aut A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2010 Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. Steiner tree Delaunay triangulation Ohlmann, Jeffrey W. aut Enthalten in Journal of heuristics Springer US, 1995 17(2010), 4 vom: 09. Juli, Seite 353-372 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:17 year:2010 number:4 day:09 month:07 pages:353-372 https://doi.org/10.1007/s10732-010-9137-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 17 2010 4 09 07 353-372 |
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10.1007/s10732-010-9137-z doi (DE-627)OLC2039387587 (DE-He213)s10732-010-9137-z-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Van Laarhoven, Jon W. verfasserin aut A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2010 Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. Steiner tree Delaunay triangulation Ohlmann, Jeffrey W. aut Enthalten in Journal of heuristics Springer US, 1995 17(2010), 4 vom: 09. Juli, Seite 353-372 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:17 year:2010 number:4 day:09 month:07 pages:353-372 https://doi.org/10.1007/s10732-010-9137-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 17 2010 4 09 07 353-372 |
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10.1007/s10732-010-9137-z doi (DE-627)OLC2039387587 (DE-He213)s10732-010-9137-z-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Van Laarhoven, Jon W. verfasserin aut A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2010 Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. Steiner tree Delaunay triangulation Ohlmann, Jeffrey W. aut Enthalten in Journal of heuristics Springer US, 1995 17(2010), 4 vom: 09. Juli, Seite 353-372 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:17 year:2010 number:4 day:09 month:07 pages:353-372 https://doi.org/10.1007/s10732-010-9137-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 17 2010 4 09 07 353-372 |
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10.1007/s10732-010-9137-z doi (DE-627)OLC2039387587 (DE-He213)s10732-010-9137-z-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Van Laarhoven, Jon W. verfasserin aut A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2010 Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. Steiner tree Delaunay triangulation Ohlmann, Jeffrey W. aut Enthalten in Journal of heuristics Springer US, 1995 17(2010), 4 vom: 09. Juli, Seite 353-372 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:17 year:2010 number:4 day:09 month:07 pages:353-372 https://doi.org/10.1007/s10732-010-9137-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 17 2010 4 09 07 353-372 |
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A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd |
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Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. © Springer Science+Business Media, LLC 2010 |
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Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. © Springer Science+Business Media, LLC 2010 |
abstract_unstemmed |
Abstract We present a heuristic for the Euclidean Steiner tree problem in ℜd for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems in ℜd for 2≤d≤5. © Springer Science+Business Media, LLC 2010 |
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The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. 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