Physical Expander in Virtual Tree Overlay

  • Taisuke Izumi
  • Maria Gradinariu Potop-Butucaru
  • Mathieu Valero
Conference paper

DOI: 10.1007/978-3-642-24100-0_6

Volume 6950 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Izumi T., Gradinariu Potop-Butucaru M., Valero M. (2011) Physical Expander in Virtual Tree Overlay. In: Peleg D. (eds) Distributed Computing. DISC 2011. Lecture Notes in Computer Science, vol 6950. Springer, Berlin, Heidelberg

Abstract

In this paper, we propose a new distributed construction of constant-degree expanders motivated by their application in P2P overlay networks and in particular in the design of robust tree overlays. Our key result can be stated as follows. Consider a complete binary tree T and construct a random pairing Π between leaf nodes and internal nodes. We prove that the graph GΠ obtained from T by contracting all pairs (leaf-internal nodes) achieves a constant node expansion with high probability. In the context of P2P overlays our result can be interpreted as follows: if each physical node participating to the tree overlay manages a random pair that couples one virtual internal node and one virtual leaf node then the physical-node layer exhibits a constant expansion with high probability. We encompass the difficulty of obtaining the random tree virtualization by proposing a local, self-organizing and churn resilient uniformly-random pairing algorithm with O(log2n) running time. Our algorithm has the merit to not modify the original tree overlay (we just control the mapping between physical nodes and virtual nodes). Therefore, our scheme is general and can be easilly extended to a large class of overlays.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Taisuke Izumi
    • 1
  • Maria Gradinariu Potop-Butucaru
    • 2
  • Mathieu Valero
    • 2
  1. 1.Graduate School of EngineeringNagoya Institute of TechnologyNagoyaJapan
  2. 2.Université Pierre et Marie Curie - Paris 6, LIP6 CNRS 7606France