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Small Stretch Spanners on Dynamic Graphs

  • Giorgio Ausiello
  • Paolo G. Franciosa
  • Giuseppe F. Italiano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

We present fully dynamic algorithms for maintaining 3- and 5-spanners of undirected graphs. For unweighted graphs we maintain a 3- or 5-spanner under insertions and deletions of edges in O(n) amortized time per operation over a sequence of Ω(n) updates. The maintained 3-spanner (resp., 5-spanner) has O(n 3/2) edges (resp., O(n 4/3) edges), which is known to be optimal. On weighted graphs with d different edge cost values, we maintain a 3- or 5-spanner in O(n) amortized time per operation over a sequence of Ω(d Open image in new window n) updates. The maintained 3-spanner (resp., 5-spanner) has O(d Open image in new window n 3/2) edges (resp., O(d Open image in new window n 4/3) edges). The same approach can be extended to graphs with real-valued edge costs in the range [1,C]. All our algorithms are deterministic and are substantially faster than recomputing a spanner from scratch after each update.

Keywords

Weighted Graph Free Edge Dynamic Graph Edge Cost Edge Deletion 
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 2005

Authors and Affiliations

  • Giorgio Ausiello
    • 1
  • Paolo G. Franciosa
    • 2
  • Giuseppe F. Italiano
    • 3
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.Dipartimento di Statistica, Probabilità e Statistiche ApplicateUniversità di Roma “La Sapienza”RomaItaly
  3. 3.Dipartimento di Informatica, Sistemi e ProduzioneUniversità di Roma “Tor Vergata”RomaItaly

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