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Improved Bounds for Minimum Fault-Tolerant Gossip Graphs

  • Toru Hasunuma
  • Hiroshi Nagamochi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6986)

Abstract

A k-fault-tolerant gossip graph is a (multiple) graph whose edges are linearly ordered such that for any ordered pair of vertices u and v, there are k + 1 edge-disjoint ascending paths from u to v. Let τ(n,k) denote the minimum number of edges in a k-fault-tolerant gossip graph with n vertices. In this paper, we present upper and lower bounds on τ(n,k) which improve the previously known bounds. In particular, from our upper bounds, it follows that \(\tau(n,k) \leq \frac{nk}{2} + O(n\log{n})\). Previously, it has been shown that this upper bound holds only for the case that n is a power of two.

Keywords

Telephone Call Exchange Path Small Factor Center Vertex Circulant Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Toru Hasunuma
    • 1
  • Hiroshi Nagamochi
    • 2
  1. 1.Institute of Socio-Arts and SciencesThe University of TokushimaTokushimaJapan
  2. 2.Department of Applied Mathematics and PhysicsKyoto UniversityKyotoJapan

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