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  Primal-Dual Approaches to the Steiner Problem

Polzin, T., & Vahdati Daneshmand, S. (2000). Primal-Dual Approaches to the Steiner Problem. In K. Jansen, & S. Khuller (Eds.), Approximation Algorithms for Combinatorial Optimization (pp. 214-225). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-33F1-D Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-33F3-9
Genre: Conference Paper

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 Creators:
Polzin, Tobias1, Author           
Vahdati Daneshmand, Siavash, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We study several old and new algorithms for computing lower and upper bounds for the Steiner problem in networks using dual-ascent and primal-dual strategies. We show that none of the known algorithms can both generate tight lower bounds empirically and guarantee their quality theoretically; and we present a new algorithm which combines both features. The new algorithm has running time $O(re\log n)$ and guarantees a ratio of at most two between the generated upper and lower bounds, whereas the fastest previous algorithm with comparably tight empirical bounds has running time $O(e^2)$ without a constant approximation ratio. Furthermore, we show that the approximation ratio two between the bounds can even be achieved in time $O(e + n\log n)$, improving the previous time bound of $O(n^2\log n)$.

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Language(s): eng - English
 Dates: 2010-03-022000
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 518185
Other: Local-ID: C1256428004B93B8-AAACDA30D457F04FC1256AA00059C715-PolzinVahdati2000
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Title: Untitled Event
Place of Event: Saarbrücken, Germany
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Title: Approximation Algorithms for Combinatorial Optimization
Source Genre: Proceedings
 Creator(s):
Jansen, Klaus1, Editor           
Khuller, Samir, Editor
Affiliations:
1 Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019            
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 214 - 225 Identifier: ISBN: 3-540-67996-0

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Title: Lecture Notes in Computer Science
Source Genre: Series
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