A variational approach to the Steiner network problem
Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Rubinstein, J. H. [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 481-499 |
|---|---|
| Übergeordnetes Werk: |
volume:33 ; year:1991 ; number:6 ; month:06 ; pages:481-499 |
| Links: |
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| DOI / URN: |
10.1007/BF02071984 |
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OLC2111116343 |
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| 520 | |a Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. | ||
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10.1007/BF02071984 doi (DE-627)OLC2111116343 (DE-He213)BF02071984-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Rubinstein, J. H. verfasserin aut A variational approach to the Steiner network problem 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. Variational Method Span Tree Variational Approach Minimal Span Tree Configuration Space Thomas, D. A. aut Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 481-499 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:481-499 https://doi.org/10.1007/BF02071984 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 06 481-499 |
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10.1007/BF02071984 doi (DE-627)OLC2111116343 (DE-He213)BF02071984-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Rubinstein, J. H. verfasserin aut A variational approach to the Steiner network problem 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. Variational Method Span Tree Variational Approach Minimal Span Tree Configuration Space Thomas, D. A. aut Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 481-499 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:481-499 https://doi.org/10.1007/BF02071984 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 06 481-499 |
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10.1007/BF02071984 doi (DE-627)OLC2111116343 (DE-He213)BF02071984-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Rubinstein, J. H. verfasserin aut A variational approach to the Steiner network problem 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. Variational Method Span Tree Variational Approach Minimal Span Tree Configuration Space Thomas, D. A. aut Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 481-499 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:481-499 https://doi.org/10.1007/BF02071984 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 06 481-499 |
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10.1007/BF02071984 doi (DE-627)OLC2111116343 (DE-He213)BF02071984-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Rubinstein, J. H. verfasserin aut A variational approach to the Steiner network problem 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. Variational Method Span Tree Variational Approach Minimal Span Tree Configuration Space Thomas, D. A. aut Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 481-499 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:481-499 https://doi.org/10.1007/BF02071984 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 06 481-499 |
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10.1007/BF02071984 doi (DE-627)OLC2111116343 (DE-He213)BF02071984-p DE-627 ger DE-627 rakwb eng 004 VZ 3,2 ssgn Rubinstein, J. H. verfasserin aut A variational approach to the Steiner network problem 1991 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Scientific Publishing Company 1991 Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. Variational Method Span Tree Variational Approach Minimal Span Tree Configuration Space Thomas, D. A. aut Enthalten in Annals of operations research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, 1984 33(1991), 6 vom: Juni, Seite 481-499 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:33 year:1991 number:6 month:06 pages:481-499 https://doi.org/10.1007/BF02071984 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 06 481-499 |
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Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. © J.C. Baltzer AG, Scientific Publishing Company 1991 |
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Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. © J.C. Baltzer AG, Scientific Publishing Company 1991 |
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Abstract Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method. © J.C. Baltzer AG, Scientific Publishing Company 1991 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2111116343</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502202346.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230502s1991 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/BF02071984</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2111116343</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)BF02071984-p</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">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">3,2</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rubinstein, J. H.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A variational approach to the Steiner network problem</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 Supposen points are given in the plane. Their coordinates form a 2n-vectorX. To study the question of finding the shortest Steiner networkS connecting these points, we allowX to vary over a configuration space. In particular, the Steiner ratio conjecture is well suited to this approach and short proofs of the casesn=4, 5 are discussed. The variational approach was used by us to solve other cases of the ratio conjecture (n=6, see [11] and for arbitraryn points lying on a circle). Recently, Du and Hwang have given a beautiful complete solution of the ratio conjecture, also using a configuration space approach but with convexity as the major idea. We have also solved Graham's problem to decide when the Steiner network is the same as the minimal spanning tree, for points on a circle and on any convex polygon, again using the variational method.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Variational Method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Span Tree</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Variational Approach</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">Configuration Space</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Thomas, D. A.</subfield><subfield code="4">aut</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 481-499</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:481-499</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/BF02071984</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">481-499</subfield></datafield></record></collection>
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