Partial is full

  • Authors:
  • Bernadette Charron-Bost;Matthias Függer;Jennifer L. Welch;Josef Widder

  • Affiliations:
  • CNRS, LIX, Ecole Polytechnique, Palaiseau;TU Wien;Texas A&M University;Texas A&M University

  • Venue:
  • SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
  • Year:
  • 2011

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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.