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Filling Logarithmic Gaps in Distributed Complexity for Global Problems

  • Hiroaki Ookawa
  • Taisuke Izumi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8939)

Abstract

Communication complexity theory is a powerful tool to show time complexity lower bounds of distributed algorithms for global problems such as minimum spanning tree (MST) and shortest path. While it often leads to nearly-tight lower bounds for many problems, polylogarithmic complexity gaps still lie between the currently best upper and lower bounds. In this paper, we propose a new approach for filling the gaps. Using this approach, we achieve tighter deterministic lower bounds for MST and shortest paths. Specifically, for those problems, we show the deterministic \(\Omega(\sqrt{n})\)-round lower bound for graphs of O(n ε ) hop-count diameter, and the deterministic \(\Omega(\sqrt{n/\log n})\) lower bound for graphs of O(logn) hop-count diameter. The main idea of our approach is to utilize the two-party communication complexity lower bound for a function we call permutation identity, which is newly introduced in this paper.

Keywords

Minimum Span Tree Communication Complexity Global Problem Permutation Identity Minimum Span Tree Algorithm 
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 2015

Authors and Affiliations

  • Hiroaki Ookawa
    • 1
  • Taisuke Izumi
    • 1
  1. 1.Nagoya Institute of TechnologyNagoyaJapan

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