Multipath Spanners via Fault-Tolerant Spanners

  • Shiri Chechik
  • Quentin Godfroy
  • David Peleg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7659)


An s-spanner H of a graph G is a subgraph such that the distance between any two vertices u and v in H is greater by at most a multiplicative factor s than the distance in G. In this paper, we focus on an extension of the concept of spanners to p-multipath distance, defined as the smallest length of a collection of p pairwise (vertex or edge) disjoint paths. The notion of multipath spanners was introduced in [15,16] for edge (respectively, vertex) disjoint paths. This paper significantly improves the stretch-size tradeoff result of the two previous papers, using the related concept of fault-tolerant s-spanners, introduced in [6] for general graphs. More precisely, we show that at the cost of increasing the number of edges by a polynomial factor in p and s, it is possible to obtain an s-multipath spanner, thereby improving on the large stretch obtained in [15,16].


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Althöfer, I., Das, G., Dobkin, D., Joseph, D., Soares, J.: On sparse spanners of weighted graphs. Discrete & Computational Geometry 9, 81–100 (1993)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Awerbuch, B., Berger, B., Cowen, L., Peleg, D.: Near-linear cost sequential and distributed constructions of sparse neighborhood covers. In: Proc. 34th IEEE FOCS, pp. 638–647 (1993)Google Scholar
  3. 3.
    Barenboim, L., Elkin, M.: Deterministic distributed vertex coloring in polylogarithmic time. In: Proc. 29th ACM PODC, pp. 410–419 (2010)Google Scholar
  4. 4.
    Baswana, S., Kavitha, T.: Faster algorithms for approximate distance oracles and all-pairs small stretch paths. In: Proc. 47th IEEE FOCS, pp. 591–602 (2006)Google Scholar
  5. 5.
    Bollobás, B., Coppersmith, D., Elkin, M.: Sparse distance preservers and additive spanners. In: Proc. 14th ACM-SIAM SODA, pp. 414–423 (2003)Google Scholar
  6. 6.
    Chechik, S., Langberg, M., Peleg, D., Roditty, L.: Fault-tolerant spanners for general graphs. In: Proc. 41st ACM STOC, pp. 435–444 (2009)Google Scholar
  7. 7.
    Cowen, L.: Compact routing with minimum stretch. J. Algo. 38, 170–183 (2001)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Cowen, L., Wagner, C.: Compact roundtrip routing in directed networks. J. Algo. 50, 79–95 (2004)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Dinitz, M., Krauthgamer, R.: Fault-Tolerant Spanners: Better and Simpler. In: Proc. 30th ACM PODC, pp. 169–178 (2011)Google Scholar
  10. 10.
    Dubhashi, D., Mei, A., Panconesi, A., Radhakrishnan, J., Srinivasan, A.: Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons. J. Computer and System Sciences 71, 467–479 (2005)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Elkin, M.: Computing almost shortest paths. ACM Tr. Algo. 1, 283–323 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Elkin, M.: A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners. In: Proc. 26th ACM PODC, pp. 185–194 (2007)Google Scholar
  13. 13.
    Elkin, M., Zhang, J.: Efficient algorithms for constructing (1 + ε,β)-spanners in the distributed and streaming models. In: Proc. 23rd ACM PODC, pp. 160–168 (2004)Google Scholar
  14. 14.
    Farley, A.M., Proskurowski, A., Zappala, D., Windisch, K.: Spanners and message distribution in networks. Discrete Applied Mathematics 137(2), 159–171 (2004)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Gavoille, C., Godfroy, Q., Viennot, L.: Multipath Spanners. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 211–223. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Gavoille, C., Godfroy, Q., Viennot, L.: Node-Disjoint Multipath Spanners and Their Relationship with Fault-Tolerant Spanners. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 143–158. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Jacquet, P., Viennot, L.: Remote spanners: what to know beyond neighbors. In: Proc. 23rd IEEE IPDPS (2009)Google Scholar
  18. 18.
    Kushman, N., Kandula, S., Katabi, D., Maggs, B.M.: R-BGP: Staying connected in a connected world. In: Proc. 4th NSDI (2007)Google Scholar
  19. 19.
    Mueller, S., Tsang, R.P., Ghosal, D.: Multipath Routing in Mobile Ad Hoc Networks: Issues and Challenges. In: Calzarossa, M.C., Gelenbe, E. (eds.) MASCOTS 2003. LNCS, vol. 2965, pp. 209–234. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Nasipuri, A., Castañeda, R., Das, S.R.: Performance of multipath routing for on-demand protocols in mobile ad hoc networks. Mobile Networks and Applications 6(4), 339–349 (2001)CrossRefMATHGoogle Scholar
  21. 21.
    Peleg, D., Scháffer, A.A.: Graph spanners. J. Graph Theory, 99–116 (1989)Google Scholar
  22. 22.
    Peleg, D., Ullman, J.D.: An optimal synchronizer for the hypercube. SIAM J. Computing 18(4), 740–747 (1989)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    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
  24. 24.
    Pan, P., Swallow, G., Atlas, A.: Fast Reroute Extensions to RSVP-TE for LSP Tunnels. RFC 4090 (Proposed Standard) (2005)Google Scholar
  25. 25.
    Roditty, L., Thorup, M., Zwick, U.: Roundtrip spanners and roundtrip routing in directed graphs. ACM Trans. Algorithms 3(4), Article 29 (2008)Google Scholar
  26. 26.
    Thorup, M., Zwick, U.: Compact routing schemes. In: Proc. SPAA, pp. 1–10 (2001)Google Scholar
  27. 27.
    Thorup, M., Zwick, U.: Approximate distance oracles. JACM 52, 1–24 (2005)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Woodruff, D.P.: Lower bounds for additive spanners, emulators, and more. In: Proc. 47th IEEE FOCS, pp. 389–398 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shiri Chechik
    • 1
  • Quentin Godfroy
    • 2
  • David Peleg
    • 3
  1. 1.Silicon Valley CenterMicrosoft ResearchUSA
  2. 2.LaBRIUniversité Bordeaux-ITalenceFrance
  3. 3.Department of Computer ScienceThe Weizmann InstituteRehovotIsrael

Personalised recommendations