Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners

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47 Scopus citations

Abstract

We present a streaming algorithm for constructing sparse spanners and show that our algorithm significantly outperforms the state-of-the-art algorithm for this task (due to Feigenbaum et al.). Specifically, the processing time per edge of our algorithm is O(1), and it is drastically smaller than that of the algorithm of Feigenbaum et al., and all other efficiency parameters of our algorithm are no greater (and some of them are strictly smaller) than the respective parameters of the state-of-the-art algorithm. We also devise a fully dynamic centralized algorithm maintaining sparse spanners. This algorithm has incremental update time of O(1), and a nontrivial decremental update time. To our knowledge, this is the first fully dynamic centralized algorithm for maintaining sparse spanners that provides nontrivial bounds on both incremental and decremental update time for a wide range of stretch parameter t.

Original languageEnglish
Article number20
JournalACM Transactions on Algorithms
Volume7
Issue number2
DOIs
StatePublished - 1 Mar 2011

Keywords

  • Graph spanners
  • Streaming algorithms

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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