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Additive Spanners: A Simple Construction

  • Mathias Bæk Tejs Knudsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

Abstract

We consider additive spanners of unweighted undirected graphs. Let G be a graph and H a subgraph of G. The most naïve way to construct an additive k-spanner of G is the following: As long as H is not an additive k-spanner repeat: Find a pair (u,v) ∈ H that violates the spanner-condition and a shortest path from u to v in G. Add the edges of this path to H.

We show that, with a very simple initial graph H, this naïve method gives additive 6- and 2-spanners of sizes matching the best known upper bounds. For additive 2-spanners we start with H = ∅ and end with O(n 3/2) edges in the spanner. For additive 6-spanners we start with H containing \(\lfloor n^{1/3} \rfloor\) arbitrary edges incident to each node and end with a spanner of size O(n 4/3).

Keywords

Short Path Triangle Inequality SIAM Journal Simple Construction 47th IEEE Symposium 
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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References

  1. 1.
    Pettie, S.: Low distortion spanners. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 78–89. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Elkin, M., Peleg, D.: (1 + ε, β)-spanner constructions for general graphs. SIAM Journal on Computing 33(3), 608–631 (2004); See also STOC 2001Google Scholar
  3. 3.
    Thorup, M., Zwick, U.: Spanners and emulators with sublinear distance errors. In: Proc. 17th ACM/SIAM Symposium on Discrete Algorithms (SODA), pp. 802–809 (2006)Google Scholar
  4. 4.
    Dor, D., Halperin, S., Zwick, U.: All-pairs almost shortest paths. SIAM Journal on Computing 29(5), 1740–1759 (2000); See also FOCS 1996Google Scholar
  5. 5.
    Baswana, S., Kavitha, T., Mehlhorn, K., Pettie, S.: New constructions of (α, β)-spanners and purely additive spanners. In: Proc. 16th ACM/SIAM Symposium on Discrete Algorithms (SODA), pp. 672–681 (2005)Google Scholar
  6. 6.
    Chechik, S.: New additive spanners. In: Proc. 24th ACM/SIAM Symposium on Discrete Algorithms (SODA), pp. 498–512 (2013)Google Scholar
  7. 7.
    Woodruff, D.P.: Lower bounds for additive spanners, emulators, and more. In: Proc. 47th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 389–398 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mathias Bæk Tejs Knudsen
    • 1
  1. 1.University of CopenhagenDenmark

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