Approximate Local Sums and Their Applications in Radio Networks

  • Zhiyu Liu
  • Maurice Herlihy
Conference paper

DOI: 10.1007/978-3-662-45174-8_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8784)
Cite this paper as:
Liu Z., Herlihy M. (2014) Approximate Local Sums and Their Applications in Radio Networks. In: Kuhn F. (eds) Distributed Computing. DISC 2014. Lecture Notes in Computer Science, vol 8784. Springer, Berlin, Heidelberg

Abstract

Although any problem in a radio network can be solved using broadcast algorithms, some problems can be solved substantially more efficiently by more specialized algorithms. This paper presents two new approximate algorithms for the local sum problem, in which each node computes a (1±ε)-approximation to the sum of the values held by its incoming neighbors (nodes that have outgoing edges to the node). We propose algorithms both with and without collision detection, as well as for the beeping model, with round complexity \(O({\log^{2} n + \log n\log m \over \epsilon^2})\), where n is the number of nodes and the value held by each node is a real number in {0} ∪ [1,m]. We then show how these algorithms can be used as building blocks to construct applications such as approximate random walk distribution, PageRank, and global sum.

Keywords

radio networks algorithms model with collision detection model without collision detection beeping model local sum random walk PageRank 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Zhiyu Liu
    • 1
  • Maurice Herlihy
    • 1
  1. 1.Department of Computer ScienceBrown UniversityUSA

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