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)


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.


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