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A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs

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Combinatorial Optimization and Applications (COCOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5573))

Abstract

The node-weighted Steiner tree problem is a variation of classical Steiner minimum tree problem. Given a graph G = (V,E) with node weight function C:V→R  +  and a subset X of V, the node-weighted Steiner tree problem is to find a Steiner tree for the set X such that its total weight is minimum. In this paper, we study this problem in unit disk graphs and present a (1+ε)-approximation algorithm for any ε> 0, when the given set of vertices is c-local. As an application, we use node-weighted Steiner tree to solve the node-weighted connected dominating set problem in unit disk graphs and obtain a (5 + ε)-approximation algorithm.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, China

    **anyue Li

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA

    Feng Zou & Weili Wu

  3. Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA

    **ao-Hua Xu, Hongwei Du & Pengjun Wan

  4. Institute of Theoretical Computer Science, Tsinghua University, Bei**g, 100084, China

    Yuexuan Wang

Authors
  1. **anyue Li
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  2. **ao-Hua Xu
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  3. Feng Zou
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  4. Hongwei Du
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  5. Pengjun Wan
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  6. Yuexuan Wang
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  7. Weili Wu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 800 West Campbell Road, TX 75080-3021, Richardson, USA

    Ding-Zhu Du

  2. Chinese Academy of Sciences, Institute of Applied Mathematics, Zhong Guan Cun Dong Lu 55, 100190, Bei**g, P. R. China

    **aodong Hu

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, FL 32611-6595, Gainesville, USA

    Panos M. Pardalos

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© 2009 Springer-Verlag Berlin Heidelberg

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Li, X. et al. (2009). A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-02026-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02025-4

  • Online ISBN: 978-3-642-02026-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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