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A new characterization of tree medians with applications to distributed algorithms

  • O. Gerstel
  • S. Zaks
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 657)

Abstract

A new characterization of tree medians is presented: we show that a vertex m is a median of a tree T with n vertices iff there exists a partition of the vertex set into ⌊n/2⌋ disjoint pairs (excluding m when n is odd), such that all the paths connecting the two vertices in any of the pairs pass through m. We show that in this case the sum of the distances between these pairs of vertices is the largest possible among all such partitions, and we use this fact to discuss lower bounds on the message complexity of the distributed sorting problem. We show that, given a network of a tree topology, choosing a median and then routing all the information through it is the best possible strategy, in terms of worst-case number of messages sent during any execution of any distributed sorting algorithm. We also discuss the implications for networks of a general topology and for the distributed ranking problem.

Keywords

Span Tree Tree Topology Ranking Problem Ranking Algorithm Tree Network 
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 1993

Authors and Affiliations

  • O. Gerstel
    • 1
  • S. Zaks
    • 1
  1. 1.Department of Computer ScienceTechnionHaifaIsrael

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