The steiner ratio for five points
Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Booth, R. S. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1991 |
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| Schlagwörter: |
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| Anmerkung: |
© J.C. Baltzer AG, Scientific Publishing Company 1991 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of operations research - Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984, 33(1991), 6 vom: Juni, Seite 419-436 |
|---|---|
| Übergeordnetes Werk: |
volume:33 ; year:1991 ; number:6 ; month:06 ; pages:419-436 |
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| DOI / URN: |
10.1007/BF02071980 |
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10.1007/BF02071980 doi (DE-627)OLC2111116300 (DE-He213)BF02071980-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Booth, R. S. verfasserin aut The steiner ratio for five points 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. Span Tree Minimal Span Tree Steiner Tree Euclidean Plane Minimal Tree Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 419-436 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:419-436 https://doi.org/10.1007/BF02071980 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT GBV_ILN_90 GBV_ILN_4029 AR 33 1991 6 06 419-436 |
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10.1007/BF02071980 doi (DE-627)OLC2111116300 (DE-He213)BF02071980-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Booth, R. S. verfasserin aut The steiner ratio for five points 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. Span Tree Minimal Span Tree Steiner Tree Euclidean Plane Minimal Tree Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 419-436 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:419-436 https://doi.org/10.1007/BF02071980 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT GBV_ILN_90 GBV_ILN_4029 AR 33 1991 6 06 419-436 |
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10.1007/BF02071980 doi (DE-627)OLC2111116300 (DE-He213)BF02071980-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Booth, R. S. verfasserin aut The steiner ratio for five points 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. Span Tree Minimal Span Tree Steiner Tree Euclidean Plane Minimal Tree Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 419-436 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:419-436 https://doi.org/10.1007/BF02071980 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT GBV_ILN_90 GBV_ILN_4029 AR 33 1991 6 06 419-436 |
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10.1007/BF02071980 doi (DE-627)OLC2111116300 (DE-He213)BF02071980-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Booth, R. S. verfasserin aut The steiner ratio for five points 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. Span Tree Minimal Span Tree Steiner Tree Euclidean Plane Minimal Tree Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 419-436 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:419-436 https://doi.org/10.1007/BF02071980 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT GBV_ILN_90 GBV_ILN_4029 AR 33 1991 6 06 419-436 |
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Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. © J.C. Baltzer AG, Scientific Publishing Company 1991 |
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Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. © J.C. Baltzer AG, Scientific Publishing Company 1991 |
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Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees. © J.C. Baltzer AG, Scientific Publishing Company 1991 |
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S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The steiner ratio for five points</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">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© J.C. Baltzer AG, Scientific Publishing Company 1991</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract It was conjectured by Gilbert and Pollak [5] 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 √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Span Tree</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Minimal Span Tree</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Steiner Tree</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Euclidean Plane</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Minimal Tree</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Annals of operations research</subfield><subfield code="d">Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984</subfield><subfield code="g">33(1991), 6 vom: Juni, Seite 419-436</subfield><subfield code="w">(DE-627)12964370X</subfield><subfield code="w">(DE-600)252629-3</subfield><subfield code="w">(DE-576)018141862</subfield><subfield code="x">0254-5330</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:33</subfield><subfield code="g">year:1991</subfield><subfield code="g">number:6</subfield><subfield code="g">month:06</subfield><subfield code="g">pages:419-436</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/BF02071980</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 code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-WIW</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4029</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">33</subfield><subfield code="j">1991</subfield><subfield code="e">6</subfield><subfield code="c">06</subfield><subfield code="h">419-436</subfield></datafield></record></collection>
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