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On the Inapproximability of Broadcasting Time

Extended Abstract
  • Christian Schindelhauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1913)

Abstract

We investigate the problem of broadcasting information in a given undirected network. At the beginning information is given at some processors, called sources. Within each time unit step every informed processor can inform only one neighboring processor. The broadcasting problem is to determine the length of the shortest broadcasting schedule for a network, called the broadcasting time of the network. We show that there is no efficient approximation algorithm for the broadcasting time of a network with a single source unless P = NP. More formally, it is NP-hard to distinguish between graphs G = (V,E) with broadcasting time smaller than \( b \in \theta \left( {\sqrt {|V|} } \right) \) and larger than \( (\tfrac{{57}} {{56}} - \varepsilon )b \) for any ∈ > 0. For ternary graphs it is NP-hard to decide whether the broadcasting time is b ε Θ(log |V|) or b + Θ(\( \sqrt b \)) in the case of multiples sources. For ternary networks with single sources, it is NP-hard to distinguish between graphs with broadcasting time smaller than \( b \in \theta \left( {\sqrt {|V|} } \right) \) and larger than \( b + c\sqrt {\log {\mathbf{ }}b} \). We prove these statements by polynomial time reductions from E3-SAT. Classification: Computational complexity, inapproximability, network communication.

Keywords

Tree Decomposition Reduction Graph Busy Schedule Binomial Tree Complete Binary Tree 
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 2000

Authors and Affiliations

  • Christian Schindelhauer
    • 1
  1. 1.International Computer Science Institute, Berkeley, USAMed. Universität zu Lübeck, Institut für Theoretische InformatikLübeckGermany

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