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Near-Linear Lower Bounds for Distributed Distance Computations, Even in Sparse Networks

  • Amir AbboudEmail author
  • Keren Censor-HillelEmail author
  • Seri KhouryEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)

Abstract

We develop a new technique for constructing sparse graphs that allow us to prove near-linear lower bounds on the round complexity of computing distances in the CONGEST model. Specifically, we show an \(\widetilde{\varOmega }(n)\) lower bound for computing the diameter in sparse networks, which was previously known only for dense networks. In fact, we can even modify our construction to obtain graphs with constant degree, using a simple but powerful degree-reduction technique which we define.

Moreover, our technique allows us to show \(\widetilde{\varOmega }(n)\) lower bounds for computing \((\frac{3}{2}-\varepsilon )\)-approximations of the diameter or the radius, and for computing a \((\frac{5}{3}-\varepsilon )\)-approximation of all eccentricities. For radius, we are unaware of any previous lower bounds. For diameter, these greatly improve upon previous lower bounds and are tight up to polylogarithmic factors, and for eccentricities the improvement is both in the lower bound and in the approximation factor.

Interestingly, our technique also allows showing an almost-linear lower bound for the verification of \((\alpha ,\beta )\)-spanners, for \(\alpha < \beta +1\).

Keywords

Distributed computing Approximations Lower bounds Diameter Radius Eccentricity Spanners 

Notes

Acknowledgement

We thank Ami Paz for many discussions and helpful suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Stanford University, Department of Computer ScienceStanfordUSA
  2. 2.Department of Computer ScienceTechnionHaifaIsrael

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