The Steiner Ratio:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
2001
|
| Series: | Combinatorial Optimization
10 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XII, 244 p) |
| ISBN: | 9781475767988 9781441948564 |
| ISSN: | 1388-3011 |
| DOI: | 10.1007/978-1-4757-6798-8 |
Staff View
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| 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 | ||
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Record in the Search Index
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| id | DE-604.BV042421705 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475767988 9781441948564 |
| issn | 1388-3011 |
| language | English |
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| physical | 1 Online-Ressource (XII, 244 p) |
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| publishDate | 2001 |
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| publisher | Springer US |
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| series2 | Combinatorial Optimization |
| spelling | Cieslik, Dietmar Verfasser aut The Steiner Ratio by Dietmar Cieslik Boston, MA Springer US 2001 1 Online-Ressource (XII, 244 p) txt rdacontent c rdamedia cr rdacarrier Combinatorial Optimization 10 1388-3011 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 Computer science Computational complexity Algorithms Discrete groups Mathematical optimization Computer Science Discrete Mathematics in Computer Science Optimization Convex and Discrete Geometry Informatik https://doi.org/10.1007/978-1-4757-6798-8 Verlag Volltext |
| 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 |
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