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Approximation Algorithms for Packing Element-Disjoint Steiner Trees on Bounded Terminal Nodes

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Algorithmic Aspects in Information and Management (AAIM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8546))

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Abstract

In this paper we discuss approximation algorithms for the Element-Disjoint Steiner Tree Packing problem (Element-STP for short). For a graph G = (V, E) and a subset of nodes T ⊆ V, called terminal nodes, a Steiner tree is a connected, acyclic subgraph that contains all the terminal nodes in T. The goal of Element-STP is to find as many element-disjoint Steiner trees as possible. Element-STP is known to be \({\cal APX}\)-hard even for |T| = 3 [1]. It is also known that Element-STP is \({\cal NP}\)-hard to approximate within a factor of Ω(log|V|) [3] and there is an O(log|V|)-approximation algorithm for Element-STP [2,4]. In this paper, we provide a \(\lceil \frac{|T|}{2}\rceil\)-approximation algorithm for Element-STP on graphs with |T| terminal nodes. Furthermore, we show that the approximation ratio of 3 for Element-STP on graphs with five terminal nodes can be improved to 2.

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Authors and Affiliations

  1. Department of Systems Design and Informatics, Kyushu Institute of Technology, Iizuka, Fukuoka, 820-8502, Japan

    Daiki Hoshika & Eiji Miyano

Authors
  1. Daiki Hoshika
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  2. Eiji Miyano
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Editor information

Editors and Affiliations

  1. School of Computing Science, Simon Fraser University, V5A 1S6, Burnaby, BC, Canada

    Qianping Gu  & Pavol Hell  & 

  2. Department of Computer Science, University of Regina, S4S 0A2, Regina, SK, Canada

    Boting Yang

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Hoshika, D., Miyano, E. (2014). Approximation Algorithms for Packing Element-Disjoint Steiner Trees on Bounded Terminal Nodes. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-07956-1_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07955-4

  • Online ISBN: 978-3-319-07956-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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