New Pairwise Spanners

Author Telikepalli Kavitha

Thumbnail PDF


  • Filesize: 0.62 MB
  • 14 pages

Document Identifiers

Author Details

Telikepalli Kavitha

Cite AsGet BibTex

Telikepalli Kavitha. New Pairwise Spanners. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 513-526, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Let G = (V,E) be an undirected unweighted graph on n vertices. A subgraph H of G is called an (all-pairs) purely additive spanner with stretch \beta if for every (u,v) \in V \times V, \mathsf{dist}_H(u,v) \le \mathsf{dist}_G(u,v) + \beta. The problem of computing sparse spanners with small stretch \beta is well-studied. Here we consider the following relaxation: we are given \p\subseteq V \times V and we seek a sparse subgraph H where \mathsf{dist}_H(u,v)\le \mathsf{dist}_G(u,v) + \beta for each (u,v) \in \p. Such a subgraph is called a pairwise spanner with additive stretch \beta and our goal is to construct such subgraphs that are sparser than all-pairs spanners with the same stretch. We show sparse pairwise spanners with additive stretch 4 and with additive stretch 6. We also consider the following special cases: \p = S \times V and \p = S \times T, where S\subseteq V and T\subseteq V, and show sparser pairwise spanners for these cases.
  • undirected graphs
  • spanners
  • approximate distances
  • additive stretch


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28(4):1167-1181, 1999. Google Scholar
  2. I. Althöfer, G. Das, D. Dobkin, D. Joseph, and J. Soares. On sparse spanners of weighted graphs. Discrete and Computational Geometry, 9:81-100, 1993. Google Scholar
  3. B. Awerbuch, B. Berger, L. Cowen, and D. Peleg. Near-linear time construction of sparse neighborhood covers. SIAM Journal on Computing, 28(1):263-277, 1998. Google Scholar
  4. B. Awerbuch and D. Peleg. Routing with polynomial communication-space trade-off. SIAM Journal on Computing, 5(2):151-162, 1992. Google Scholar
  5. S. Baswana and T. Kavitha. Faster algorithms for all-pairs approximate shortest paths in undirected graphs. SIAM Journal on Computing, 39(7):2865-2896, 2010. Google Scholar
  6. S. Baswana, T. Kavitha, K. Mehlhorn, and S. Pettie. Additive spanners and (α,β)-spanners. ACM Transactions on Algorithms, 7(1), 2010. Google Scholar
  7. S. Baswana and S. Sen. Approximate distance oracles for unweighted graphs in o(n²log n) time. ACM Transactions on Algorithms, 2(4):557-577, 2006. Google Scholar
  8. S. Baswana and S. Sen. A simple linear time algorithm for computing a (2k-1)-spanner of o(n^1+1/k) size in weighted graphs. Random Structures and Algorithms, 30(4):532-563, 2007. Google Scholar
  9. B. Bollobás, D. Coppersmith, and M. Elkin. Sparse distance preservers and additive spanners. SIAM Journal on Discrete Math., 19(4):1029-1055, 2005. Google Scholar
  10. S. Chechik. New additive spanners. In Proceedings of the 24th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 498-512, 2013. Google Scholar
  11. E. Cohen. Fast algorithms for constructing t-spanners and paths of stretch t. In Proceedings of the 34th IEEE Symp. on Foundations of Computer Science (FOCS), pages 648-658, 1993. Google Scholar
  12. D. Coppersmith and M. Elkin. Sparse source-wise and pair-wise distance preservers. In Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 660-669, 2005. Google Scholar
  13. L. J. Cowen. Compact routing with minimum stretch. Journal of Algorithms, 28:170-183, 2001. Google Scholar
  14. L. J. Cowen and C. G. Wagner. Compact roundtrip routing in directed networks. Journal of Algorithms, 50(1):79-95, 2004. Google Scholar
  15. M. Cygan, F. Grandoni, and T. Kavitha. On pairwise spanners. In Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (STACS), pages 209-220, 2013. Google Scholar
  16. D. Dor, S. Halperin, and U. Zwick. All-pairs almost shortest paths. SIAM Journal on Computing, 29(5):1740-1759, 2004. Google Scholar
  17. M. Elkin. Computing almost shortest paths. ACM Transactions on Algorithms, 1(2):283-323, 2005. Google Scholar
  18. M. Elkin and D. Peleg. (1 + ε, β)-spanner construction for general graphs. SIAM Journal on Computing, 33(3):608-631, 2004. Google Scholar
  19. C. Gavoille, D. Peleg, S. Perennes, and R. Raz. Distance labeling in graphs. In Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 210-219, 2001. Google Scholar
  20. T. Kavitha and N. M. Varma. Small stretch pairwise spanners. In Proceedings of the 40th International Colloquium on Automata, Languages and Programming (ICALP), pages 601-612, 2013. Google Scholar
  21. M. Parter. Bypassing Erdős' girth conjecture: Hybrid spanners and sourcewise spanners. In Proceedings of the 41st International Colloquium on Automata, Languages and Programming (ICALP), pages 608-619, 2014. Google Scholar
  22. D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33(3):167-176, 2000. Google Scholar
  23. D. Peleg and A. A. Schaffer. Graph spanners. Journal of Graph Theory, 13:99-116, 1989. Google Scholar
  24. D. Peleg and J. D. Ullman. An optimal synchronizer for the hypercube. SIAM Journal on Computing, 18:740-747, 1989. Google Scholar
  25. S. Pettie. Low distortion spanners. ACM Transactions on Algorithms, 6(1), 2009. Google Scholar
  26. L. Roditty, M. Thorup, and U. Zwick. Deterministic constructions of approximate distance oracles and spanners. In Proceedings of the 32nd Int. Colloq. on Automata, Languages, and Programming (ICALP), pages 261-272, 2005. Google Scholar
  27. L. Roditty and U. Zwick. On dynamic shortest paths problems. In Proceedings of the 12th Annual European Symposium on Algorithms (ESA), pages 580-591, 2004. Google Scholar
  28. M. Thorup and U. Zwick. Approximate distance oracles. Journal of the ACM, 52(1):1-24, 2005. Google Scholar
  29. D. P. Woodruff. Additive spanners in nearly quadratic time. In Proceedings of the 37th Int. Colloq. on Automata, Languages, and Programming (ICALP), pages 463-474, 2010. Google Scholar