Dynamic Algorithms for Graph Spanners

  • Surender Baswana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


Let G=(V,E) be an undirected weighted graph on |V|=n vertices and |E|=m edges. For the graph G, A spanner with stretch t∈ℕ is a subgraph (V,E S ), E S  ⊆ E, such that the distance between any pair of vertices in this subgraph is at most t times the distance between them in the graph G. We present simple and efficient dynamic algorithms for maintaining spanners with essentially optimal (expected) size versus stretch trade-off for any given unweighted graph. The main result is a decremental algorithm that takes expected \(O(\mathop{\mathrm{polylog}} n)\) time per edge deletion for maintaining a spanner with arbitrary stretch. This algorithm easily leads to a fully dynamic algorithm with sublinear (in n) time per edge insertion or deletion. Quite interestingly, this paper also reports that for stretch at most 6, it is possible to maintain a spanner fully dynamically with expected constant time per update. All these algorithms use simple randomization techniques on the top of an existing static algorithm [6] for computing spanners, and achieve drastic improvement over the previous best deterministic dynamic algorithms for spanners.


Hash Table Weighted Graph Dynamic Algorithm Edge Deletion Unweighted Graph 
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 2006

Authors and Affiliations

  • Surender Baswana
    • 1
  1. 1.Max-Planck Institute for Computer ScienceSaarbrückenGermany

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