Analytic formulas for full steiner trees
Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this p...
Ausführliche Beschreibung
Autor*in: |
Booth, R. S. [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
1991 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Discrete & computational geometry - New York, NY : Springer, 1986, 6(1991), 1 vom: März, Seite 69-82 |
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Übergeordnetes Werk: |
volume:6 ; year:1991 ; number:1 ; month:03 ; pages:69-82 |
Links: |
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DOI / URN: |
10.1007/BF02574675 |
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Katalog-ID: |
SPR006185797 |
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520 | |a Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. | ||
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10.1007/BF02574675 doi (DE-627)SPR006185797 (SPR)BF02574675-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 004 ASE 31.59 bkl 31.12 bkl 31.76 bkl Booth, R. S. verfasserin aut Analytic formulas for full steiner trees 1991 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. Span Tree (dpeaa)DE-He213 Analytic Formula (dpeaa)DE-He213 Minimal Span Tree (dpeaa)DE-He213 Equilateral Triangle (dpeaa)DE-He213 Steiner Tree (dpeaa)DE-He213 Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 6(1991), 1 vom: März, Seite 69-82 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:6 year:1991 number:1 month:03 pages:69-82 https://dx.doi.org/10.1007/BF02574675 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.59 ASE 31.12 ASE 31.76 ASE AR 6 1991 1 03 69-82 |
spelling |
10.1007/BF02574675 doi (DE-627)SPR006185797 (SPR)BF02574675-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 004 ASE 31.59 bkl 31.12 bkl 31.76 bkl Booth, R. S. verfasserin aut Analytic formulas for full steiner trees 1991 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. Span Tree (dpeaa)DE-He213 Analytic Formula (dpeaa)DE-He213 Minimal Span Tree (dpeaa)DE-He213 Equilateral Triangle (dpeaa)DE-He213 Steiner Tree (dpeaa)DE-He213 Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 6(1991), 1 vom: März, Seite 69-82 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:6 year:1991 number:1 month:03 pages:69-82 https://dx.doi.org/10.1007/BF02574675 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.59 ASE 31.12 ASE 31.76 ASE AR 6 1991 1 03 69-82 |
allfields_unstemmed |
10.1007/BF02574675 doi (DE-627)SPR006185797 (SPR)BF02574675-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 004 ASE 31.59 bkl 31.12 bkl 31.76 bkl Booth, R. S. verfasserin aut Analytic formulas for full steiner trees 1991 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. Span Tree (dpeaa)DE-He213 Analytic Formula (dpeaa)DE-He213 Minimal Span Tree (dpeaa)DE-He213 Equilateral Triangle (dpeaa)DE-He213 Steiner Tree (dpeaa)DE-He213 Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 6(1991), 1 vom: März, Seite 69-82 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:6 year:1991 number:1 month:03 pages:69-82 https://dx.doi.org/10.1007/BF02574675 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.59 ASE 31.12 ASE 31.76 ASE AR 6 1991 1 03 69-82 |
allfieldsGer |
10.1007/BF02574675 doi (DE-627)SPR006185797 (SPR)BF02574675-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 004 ASE 31.59 bkl 31.12 bkl 31.76 bkl Booth, R. S. verfasserin aut Analytic formulas for full steiner trees 1991 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. Span Tree (dpeaa)DE-He213 Analytic Formula (dpeaa)DE-He213 Minimal Span Tree (dpeaa)DE-He213 Equilateral Triangle (dpeaa)DE-He213 Steiner Tree (dpeaa)DE-He213 Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 6(1991), 1 vom: März, Seite 69-82 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:6 year:1991 number:1 month:03 pages:69-82 https://dx.doi.org/10.1007/BF02574675 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.59 ASE 31.12 ASE 31.76 ASE AR 6 1991 1 03 69-82 |
allfieldsSound |
10.1007/BF02574675 doi (DE-627)SPR006185797 (SPR)BF02574675-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 004 ASE 31.59 bkl 31.12 bkl 31.76 bkl Booth, R. S. verfasserin aut Analytic formulas for full steiner trees 1991 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. Span Tree (dpeaa)DE-He213 Analytic Formula (dpeaa)DE-He213 Minimal Span Tree (dpeaa)DE-He213 Equilateral Triangle (dpeaa)DE-He213 Steiner Tree (dpeaa)DE-He213 Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 6(1991), 1 vom: März, Seite 69-82 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:6 year:1991 number:1 month:03 pages:69-82 https://dx.doi.org/10.1007/BF02574675 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.59 ASE 31.12 ASE 31.76 ASE AR 6 1991 1 03 69-82 |
language |
English |
source |
Enthalten in Discrete & computational geometry 6(1991), 1 vom: März, Seite 69-82 volume:6 year:1991 number:1 month:03 pages:69-82 |
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Enthalten in Discrete & computational geometry 6(1991), 1 vom: März, Seite 69-82 volume:6 year:1991 number:1 month:03 pages:69-82 |
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Discrete & computational geometry |
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Booth, R. S. @@aut@@ |
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Booth, R. S. |
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510 004 ASE 31.59 bkl 31.12 bkl 31.76 bkl Analytic formulas for full steiner trees Span Tree (dpeaa)DE-He213 Analytic Formula (dpeaa)DE-He213 Minimal Span Tree (dpeaa)DE-He213 Equilateral Triangle (dpeaa)DE-He213 Steiner Tree (dpeaa)DE-He213 |
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analytic formulas for full steiner trees |
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Analytic formulas for full steiner trees |
abstract |
Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. |
abstractGer |
Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. |
abstract_unstemmed |
Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons. |
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Analytic formulas for full steiner trees |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006185797</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110185420.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201002s1991 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/BF02574675</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006185797</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)BF02574675-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">004</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">004</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.59</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.12</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.76</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Booth, R. S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Analytic formulas for full steiner trees</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1991</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract It was conjectured by Gilbert and Pollak [6] that, for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least%$\sqrt 3 /2%$. To date, this has been proved only for at most five points. In this paper, some analytic formulas for the length of full Steiner trees are considered. These provide an alternative proof of the conjecture for quadrilaterals, and the foundation for a possible approach for more complicated polygons.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Span Tree</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analytic Formula</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Minimal Span Tree</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Equilateral Triangle</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Steiner Tree</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Discrete & computational geometry</subfield><subfield code="d">New York, NY : Springer, 1986</subfield><subfield code="g">6(1991), 1 vom: März, Seite 69-82</subfield><subfield code="w">(DE-627)253722330</subfield><subfield code="w">(DE-600)1459007-4</subfield><subfield code="x">1432-0444</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:6</subfield><subfield code="g">year:1991</subfield><subfield code="g">number:1</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:69-82</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/BF02574675</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield 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