The Steiner tree problem
The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the ori...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
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Amsterdam
North-Holland
1992, 1992
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| Series: | Annals of discrete mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
| Summary: | The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging. The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole |
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| Physical Description: | xi, 339 pages illustrations |
| ISBN: | 0080867936 9786611789688 1281789682 9780080867939 9781281789686 044489098X 9780444890986 |