Steiner Minimal Trees:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
1998
|
| Series: | Nonconvex Optimization and Its Applications
23 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone |
| Physical Description: | 1 Online-Ressource (XII, 322 p) |
| ISBN: | 9781475765854 9781441947901 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/978-1-4757-6585-4 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421697 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1998 |||| o||u| ||||||eng d | ||
| 020 | |a 9781475765854 |c Online |9 978-1-4757-6585-4 | ||
| 020 | |a 9781441947901 |c Print |9 978-1-4419-4790-1 | ||
| 024 | 7 | |a 10.1007/978-1-4757-6585-4 |2 doi | |
| 035 | |a (OCoLC)1184506385 | ||
| 035 | |a (DE-599)BVBBV042421697 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 004.0151 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Cieslik, Dietmar |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Steiner Minimal Trees |c by Dietmar Cieslik |
| 264 | 1 | |a Boston, MA |b Springer US |c 1998 | |
| 300 | |a 1 Online-Ressource (XII, 322 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Nonconvex Optimization and Its Applications |v 23 |x 1571-568X | |
| 500 | |a The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone | ||
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Discrete groups | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Computer Science | |
| 650 | 4 | |a Discrete Mathematics in Computer Science | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a Convex and Discrete Geometry | |
| 650 | 4 | |a Informatik | |
| 650 | 0 | 7 | |a Steiner-Baum |0 (DE-588)4228498-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Steiner-Baum |0 (DE-588)4228498-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4757-6585-4 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027857114 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153095064649728 |
|---|---|
| any_adam_object | |
| author | Cieslik, Dietmar |
| author_facet | Cieslik, Dietmar |
| author_role | aut |
| author_sort | Cieslik, Dietmar |
| author_variant | d c dc |
| building | Verbundindex |
| bvnumber | BV042421697 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184506385 (DE-599)BVBBV042421697 |
| dewey-full | 004.0151 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.0151 |
| dewey-search | 004.0151 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| doi_str_mv | 10.1007/978-1-4757-6585-4 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03103nmm a2200517zcb4500</leader><controlfield tag="001">BV042421697</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1998 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781475765854</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4757-6585-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441947901</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4419-4790-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4757-6585-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184506385</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421697</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">004.0151</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cieslik, Dietmar</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Steiner Minimal Trees</subfield><subfield code="c">by Dietmar Cieslik</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Springer US</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 322 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Nonconvex Optimization and Its Applications</subfield><subfield code="v">23</subfield><subfield code="x">1571-568X</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete Mathematics in Computer Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex and Discrete Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Steiner-Baum</subfield><subfield code="0">(DE-588)4228498-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Steiner-Baum</subfield><subfield code="0">(DE-588)4228498-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4757-6585-4</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857114</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042421697 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475765854 9781441947901 |
| issn | 1571-568X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857114 |
| oclc_num | 1184506385 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 322 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer US |
| record_format | marc |
| series2 | Nonconvex Optimization and Its Applications |
| spelling | Cieslik, Dietmar Verfasser aut Steiner Minimal Trees by Dietmar Cieslik Boston, MA Springer US 1998 1 Online-Ressource (XII, 322 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 23 1571-568X The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone Computer science Computational complexity Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik Steiner-Baum (DE-588)4228498-3 gnd rswk-swf Steiner-Baum (DE-588)4228498-3 s 1\p DE-604 https://doi.org/10.1007/978-1-4757-6585-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cieslik, Dietmar Steiner Minimal Trees Computer science Computational complexity Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik Steiner-Baum (DE-588)4228498-3 gnd |
| subject_GND | (DE-588)4228498-3 |
| title | Steiner Minimal Trees |
| title_auth | Steiner Minimal Trees |
| title_exact_search | Steiner Minimal Trees |
| title_full | Steiner Minimal Trees by Dietmar Cieslik |
| title_fullStr | Steiner Minimal Trees by Dietmar Cieslik |
| title_full_unstemmed | Steiner Minimal Trees by Dietmar Cieslik |
| title_short | Steiner Minimal Trees |
| title_sort | steiner minimal trees |
| topic | Computer science Computational complexity Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik Steiner-Baum (DE-588)4228498-3 gnd |
| topic_facet | Computer science Computational complexity Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik Steiner-Baum |
| url | https://doi.org/10.1007/978-1-4757-6585-4 |
| work_keys_str_mv | AT cieslikdietmar steinerminimaltrees |