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On the Integrality Gap of a Natural Formulation of the Single-sink Buy-at-Bulk Network Design Problem

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Integer Programming and Combinatorial Optimization (IPCO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2081))

Abstract

We study two versions of the single sink buy-at-bulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of flow to be routed to the sink. We are also given a finite set of cable types which have different cost characteristics and obey the principle of economies of scale. We wish to construct a minimum cost network to support the demands, using our given cable types. We study a natural integer program formulation of the problem, and show that its integrality gap is O(k), where k is the number of cable types. As a consequence, we also provide an O(k)-approximation algorithm.

This research was supported by a faculty development grant awarded to R. Ravi by the Carnegie Bosch Institute, Carnegie Mellon University, Pittsburgh PA 15213-3890.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, New Delhi, India

    Naveen Garg & Rohit Khandekar

  2. Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85287, USA

    Goran Konjevod

  3. GSIA, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA

    R. Ravi & Amitabh Sinha

  4. Krannert School of Management, Purdue University, West Lafayette, IN 47907, USA

    F. S. Salman

Authors
  1. Naveen Garg
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  2. Rohit Khandekar
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  3. Goran Konjevod
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  4. R. Ravi
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  5. F. S. Salman
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  6. Amitabh Sinha
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Editor information

Editors and Affiliations

  1. Instituut voor Informatica en Informatiekunde, Universiteit Utrecht, Padualaan 14, 3584, CH Utrecht, The Netherlands

    Karen Aardal

  2. CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Bert Gerards

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© 2001 Springer-Verlag Berlin Heidelberg

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Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F.S., Sinha, A. (2001). On the Integrality Gap of a Natural Formulation of the Single-sink Buy-at-Bulk Network Design Problem. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_14

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  • DOI: https://doi.org/10.1007/3-540-45535-3_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42225-9

  • Online ISBN: 978-3-540-45535-6

  • eBook Packages: Springer Book Archive

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