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Communication in Networks with Random Dependent Faults

  • Evangelos Kranakis
  • Michel Paquette
  • Andrzej Pelc
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)

Abstract

The aim of this paper is to study communication in networks where nodes fail in a random dependent way. In order to capture fault dependencies, we introduce the neighborhood fault model, where damaging events, called spots, occur randomly and independently with probability p at nodes of a network, and cause faults in the given node and all of its neighbors. Faults at distance at most 2 become dependent in this model and are positively correlated. We investigate the impact of spot probability on feasibility and time of communication in the fault-free part of the network. We show a network which supports fast communication with high probability, if p ≤ 1/clogn. We also show that communication is not feasible with high probability in most classes of networks, for constant spot probabilities. For smaller spot probabilities, high probability communication is supported even by bounded degree networks. It is shown that the torus supports communication with high probability when p decreases faster than 1/n 1/2, and does not when p ∈ 1/O(n 1/2). Furthermore, a network built of tori is designed, with the same fault-tolerance properties and additionally supporting fast communication. We show, however, that networks of degree bounded by a constant d do not support communication with high probability, if p ∈ 1/O(n 1/d ). While communication in networks with independent faults was widely studied, this is the first analytic paper which investigates network communication for random dependent faults.

Keywords

Fault-tolerance dependent faults communication crash faults network connectivity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Evangelos Kranakis
    • 1
  • Michel Paquette
    • 1
  • Andrzej Pelc
    • 2
  1. 1.School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6Canada
  2. 2.Département d’informatique et d’ingénierie, Université du Québec en Outaouais. Gatineau, Québec, J8X 3X7Canada

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