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k-Robust Single-Message Transmission

Extended Abstract
  • André Kündgen
  • Michael J. Pelsmajer
  • Radhika Ramamurthi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3405)

Abstract

End-to-end communication considers the problem of sending messages between a sender s and a receiver r through an asynchronous, unreliable network, such as the Internet. We consider the problem of transmitting a single message from s to r through a network in which edges may fail and cannot recover. We assume that some s,r-path survives, but we do not know which path it is. A routing algorithm is k-robust if it ensures that a message sent by s will be received by r when at most k edges fail, and it will never generate an infinite number of messages. Graphs with a k-robust algorithm for all k were characterized in[5]. For any other graph, its robustness is the maximum k for which it has a k-robust algorithm.

We provide general lower bounds for robustness by improving a natural algorithm obtained from Menger’s Theorem. We determine robustness for several examples, such as complete graphs, grids, and hypercubes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • André Kündgen
    • 1
  • Michael J. Pelsmajer
    • 2
  • Radhika Ramamurthi
    • 1
  1. 1.Department of MathematicsCalifornia State UniversitySan Marcos
  2. 2.Department of Applied MathematicsIllinois Institute of Technology 

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