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Deterministic Dominating Set Construction in Networks with Bounded Degree

  • Conference paper
Distributed Computing and Networking (ICDCN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6522))

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Abstract

This paper considers the problem of calculating dominating sets in networks with bounded degree. In these networks, the maximal degree of any node is bounded by Δ, which is usually significantly smaller than n, the total number of nodes in the system. Such networks arise in various settings of wireless and peer-to-peer communication. A trivial approach of choosing all nodes into the dominating set yields an algorithm with the approximation ratio of Δ + 1. We show that any deterministic algorithm with non-trivial approximation ratio requires Ω(log* n) rounds, meaning effectively that no o(Δ)-approximation deterministic algorithm with a running time independent of the size of the system may ever exist. On the positive side, we show two deterministic algorithms that achieve logΔ and 2logΔ-approximation in O(Δ3 + log* n) and O(Δ2logΔ + log* n) time, respectively. These algorithms rely on coloring rather than node IDs to break symmetry.

This work is partially supported by the Israeli Science Foundation grant 1247/09 and by the Technion Hasso Plattner Center.

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Authors and Affiliations

  1. Department of Computer Science, Technion, Israel

    Roy Friedman & Alex Kogan

Authors
  1. Roy Friedman
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  2. Alex Kogan
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Editor information

Editors and Affiliations

  1. Microsoft Research Silicon Valley, 1065 La Avenida – bldg. 6, 94043, Mountain View, CA, USA

    Marcos K. Aguilera

  2. School of Computing, National University of Singapore, COM2-04-25, 15 Computing Drive, 117418, Republic of Singapore

    Haifeng Yu

  3. 458 Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, MC-228, 1308 West Main Street, 61801, Urbana, IL, USA

    Nitin H. Vaidya

  4. Alcatel-Lucent Technologies, Manyata Technology Park, Nagawara, 560045, Bangalore, India

    Vikram Srinivasan

  5. ECE Department, Duke University, 130 Hudson Hall, Box 90291, 27708, Durham, NC, USA

    Romit Roy Choudhury

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Friedman, R., Kogan, A. (2011). Deterministic Dominating Set Construction in Networks with Bounded Degree. In: Aguilera, M.K., Yu, H., Vaidya, N.H., Srinivasan, V., Choudhury, R.R. (eds) Distributed Computing and Networking. ICDCN 2011. Lecture Notes in Computer Science, vol 6522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17679-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-17679-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17678-4

  • Online ISBN: 978-3-642-17679-1

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