Partial is Full

  • Bernadette Charron-Bost
  • Matthias Függer
  • Jennifer L. Welch
  • Josef Widder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6796)

Abstract

Link reversal is the basis of several well-known routing algorithms [1,2,3]. In these algorithms, logical directions are imposed on the communication links and a node that becomes a sink reverses some of its incident links to allow the (re)construction of paths to the destination. In the Full Reversal (FR) algorithm [1], a sink reverses all its incident links. In other schemes, a sink reverses only some of its incident links; a notable example is the Partial Reversal (PR) algorithm [1]. Prior work [4] has introduced a generalization, called LR, of link-reversal routing, including FR and PR. In this paper, we show that every execution of LR on any link-labeled input graph corresponds, in a precise sense, to an execution of FR on a transformed graph. Thus, all the link reversal schemes captured by LR can be reduced to FR, indicating that “partial is full.” The correspondence preserves the work and time complexities. As a result, we can, for the first time, obtain the exact time complexity for LR, and by specialization for PR.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bernadette Charron-Bost
    • 1
  • Matthias Függer
    • 2
  • Jennifer L. Welch
    • 3
  • Josef Widder
    • 3
  1. 1.CNRS, LIX, Ecole polytechniquePalaiseauFrance
  2. 2.TU WienAustria
  3. 3.Texas A&M UniversityUSA

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