The Steiner Ratio:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston, MA
Springer US
2001
|
| Schriftenreihe: | Combinatorial Optimization
10 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-1-4757-6798-8 |
| Beschreibung: | Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms |
| Umfang: | 1 Online-Ressource (XII, 244 p) |
| ISBN: | 9781475767988 9781441948564 |
| ISSN: | 1388-3011 |
| DOI: | 10.1007/978-1-4757-6798-8 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421705 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2001 xx o|||| 00||| eng d | ||
| 020 | |a 9781475767988 |c Online |9 978-1-4757-6798-8 | ||
| 020 | |a 9781441948564 |c Print |9 978-1-4419-4856-4 | ||
| 024 | 7 | |a 10.1007/978-1-4757-6798-8 |2 doi | |
| 035 | |a (OCoLC)863930494 | ||
| 035 | |a (DE-599)BVBBV042421705 | ||
| 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 The Steiner Ratio |c by Dietmar Cieslik |
| 264 | 1 | |a Boston, MA |b Springer US |c 2001 | |
| 300 | |a 1 Online-Ressource (XII, 244 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Combinatorial Optimization |v 10 |x 1388-3011 | |
| 500 | |a Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms | ||
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Algorithms | |
| 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 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4757-6798-8 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027857122 | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 2068714 |
|---|---|
| _version_ | 1821931222593437696 |
| 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 | BV042421705 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863930494 (DE-599)BVBBV042421705 |
| 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 | 10.1007/978-1-4757-6798-8 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02688nam a2200493zcb4500</leader><controlfield tag="001">BV042421705</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2001 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781475767988</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4757-6798-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441948564</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4419-4856-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4757-6798-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863930494</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421705</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">The Steiner Ratio</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">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 244 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">Combinatorial Optimization</subfield><subfield code="v">10</subfield><subfield code="x">1388-3011</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms</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">Algorithms</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="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4757-6798-8</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><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="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857122</subfield></datafield></record></collection> |
| id | DE-604.BV042421705 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:45Z |
| institution | BVB |
| isbn | 9781475767988 9781441948564 |
| issn | 1388-3011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857122 |
| oclc_num | 863930494 |
| 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, 244 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer US |
| record_format | marc |
| series2 | Combinatorial Optimization |
| spellingShingle | Cieslik, Dietmar The Steiner Ratio Computer science Computational complexity Algorithms Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik |
| title | The Steiner Ratio |
| title_auth | The Steiner Ratio |
| title_exact_search | The Steiner Ratio |
| title_full | The Steiner Ratio by Dietmar Cieslik |
| title_fullStr | The Steiner Ratio by Dietmar Cieslik |
| title_full_unstemmed | The Steiner Ratio by Dietmar Cieslik |
| title_short | The Steiner Ratio |
| title_sort | the steiner ratio |
| topic | Computer science Computational complexity Algorithms Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik |
| topic_facet | Computer science Computational complexity Algorithms Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik |
| url | https://doi.org/10.1007/978-1-4757-6798-8 |
| work_keys_str_mv | AT cieslikdietmar thesteinerratio |