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Resilient and Low Stretch Routing through Embedding into Tree Metrics

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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Abstract

Given a network, the simplest routing scheme is probably routing on a spanning tree. This method however does not provide good stretch — the route between two nodes can be much longer than their shortest distance, nor does it give good resilience — one node failure may disconnect quadratically many pairs. In this paper we use two trees to achieve both constant stretch and good resilience. Given a metric (e.g., as the shortest path metric of a given communication network), we build two hierarchical well-separated trees using randomization such that for any two nodes u, v, the shorter path of the two paths in the two respective trees gives a constant stretch of the metric distance of u, v, and the removal of any node only disconnect the routes between O(1/n) fraction of all pairs. Both bounds are in expectation and hold true as long as the metric follows certain geometric growth rate (the number of nodes within distance r is a polynomial function of r), which holds for many realistic network settings such as wireless ad hoc networks and Internet backbone graphs. The algorithms have been implemented and tested on real data.

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References

  1. Abraham, I., Gavoille, C., Goldberg, A.V., Malkhi, D.: Routing in networks with low doubling dimension. In: Proc. of the 26th International Conference on Distributed Computing Systems (ICDCS) (July 2006)

    Google Scholar 

  2. Abraham, I., Malkhi, D.: Name independent routing for growth bounded networks. In: SPAA 2005: Proceedings of the Seventeenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 49–55 (2005)

    Google Scholar 

  3. Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest common ancestors: a survey and a new distributed algorithm. In: SPAA 2002: Proceedings of the Fourteenth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 258–264 (2002)

    Google Scholar 

  4. Atlas, A., Zinin, A.: Basic specification for ip fast reroute: Loop-free alternates. In: IETF RFC 5286 (September 2008)

    Google Scholar 

  5. Bartal, Y.: Probabilistic approximation of metric spaces and its algorithmic applications. In: FOCS 1996: Proceedings of the 37th Annual Symposium on Foundations of Computer Science, p. 184 (1996)

    Google Scholar 

  6. Bartal, Y.: On approximating arbitrary metrices by tree metrics. In: STOC 1998: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 161–168 (1998)

    Google Scholar 

  7. Reichert, Y.G.C., Magedanz, T.: Two routing algorithms for failure protection in ip networks. In: Proc. ISCC (2005)

    Google Scholar 

  8. Chan, H.T.-H., Gupta, A., Maggs, B.M., Zhou, S.: On hierarchical routing in doubling metrics. In: SODA 2005: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 762–771 (2005)

    Google Scholar 

  9. Cowen, L.J.: Compact routing with minimum stretch. In: SODA 1999: Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 255–260 (1999)

    Google Scholar 

  10. Eilam, T., Gavoille, C., Peleg, D.: Compact routing schemes with low stretch factor. J. Algorithms 46(2), 97–114 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: STOC 2003: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 448–455 (2003)

    Google Scholar 

  12. Gao, J., Guibas, L.J., Milosavljevic, N., Zhou, D.: Distributed resource management and matching in sensor networks. In: Proc. of the 8th International Symposium on Information Processing in Sensor Networks (IPSN 2009), pp. 97–108 (April 2009)

    Google Scholar 

  13. Gao, J., Zhang, L.: Tradeoffs between stretch factor and load balancing ratio in routing on growth restricted graphs. IEEE Transactions on Parallel and Distributed Computing 20(2), 171–179 (2009)

    Article  Google Scholar 

  14. Gottlieb, L.-A., Roditty, L.: Improved algorithms for fully dynamic geometric spanners and geometric routing. In: SODA 2008: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2008)

    Google Scholar 

  15. Gupta, A., Krauthgamer, R., Lee, J.R.: Bounded geometries, fractals, and low-distortion embeddings. In: FOCS 2003: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 534–543 (2003)

    Google Scholar 

  16. Karger, D., Ruhl, M.: Find nearest neighbors in growth-restricted metrics. In: Proc. ACM Symposium on Theory of Computing, pp. 741–750 (2002)

    Google Scholar 

  17. Konjevod, G., Richa, A.W., Xia, D.: Optimal-stretch name-independent compact routing in doubling metrics. In: PODC 2006: Proceedings of the Twenty-Fifth Annual ACM Symposium on Principles of Distributed Computing, pp. 198–207 (2006)

    Google Scholar 

  18. Linial, N., London, E., Rabinovich, Y.: The geometry of graphs and some of its algorithmic applications. Combinatorica 15, 215–245 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. Motiwala, M., Elmore, M., Feamster, N., Vempala, S.: Path splicing. SIGCOMM Comput. Commun. Rev. 38(4), 27–38 (2008)

    Article  Google Scholar 

  20. Motskin, A., Downes, I., Kusy, B., Gnawali, O., Guibas, L.: Network Warehouses: Efficient Information Distribution to Mobile Users. In: Proc. of the 30th Annual IEEE Conference on Computer Communications (INFOCOM) (April 2011)

    Google Scholar 

  21. Neelesh Khanna, S.B.: Approximate shortest paths avoiding a failed vertex: Optimal size data structures for unweighted graphs. In: STACS, pp. 513–524 (2010)

    Google Scholar 

  22. Ng, E., Zhang, H.: Predicting Internet network distance with coordinates-based approaches. In: Proc. IEEE INFOCOM, pp. 170–179 (2002)

    Google Scholar 

  23. Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications (2000)

    Google Scholar 

  24. Plaxton, C.G., Rajaraman, R., Richa, A.W.: Accessing nearby copies of replicated objects in a distributed environment. In: Proc. ACM Symposium on Parallel Algorithms and Architectures, pp. 311–320 (1997)

    Google Scholar 

  25. Raghavan, P., Thompson, C.D.: Provably good routing in graphs: regular arrays. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 79–87 (1985)

    Google Scholar 

  26. Ray, K.-W.K.S., Guerin, R., Sofia, R.: Always acyclic distributed path computation. To appear in IEEE/ACM Transactions on Networking (2009)

    Google Scholar 

  27. Sarkar, R., Zhu, X., Gao, J.: Spatial distribution in routing table design for sensor networks. In: Proc. of the 28th Annual IEEE Conference on Computer Communications (INFOCOM 2009), Mini-Conference (April 2009)

    Google Scholar 

  28. Shand, M., Bryant, S.: Ip fast reroute framework. In: Internet Draft (June 2009)

    Google Scholar 

  29. Spring, N., Mahajan, R., Wetherall, D., Anderson, T.: Measuring isp topologies with rocketfuel. IEEE/ACM Trans. Netw. 12(1), 2–16 (2004)

    Article  Google Scholar 

  30. Thorup, M., Zwick, U.: Compact routing schemes. In: SPAA 2001: Proceedings of the Thirteenth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 1–10 (2001)

    Google Scholar 

  31. Ohara, S.I.Y., Meter, R.V.: Mara: Maximum alternative routing algorithm. In: Proc. IEEE INFOCOM (2009)

    Google Scholar 

  32. Zhou, D., Gao, J.: Maintaining approximate minimum steiner tree and k-center for mobile agents in a sensor network. In: Proc. of the 29th Annual IEEE Conference on Computer Communications (INFOCOM 2010) (March 2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, NY, 11794, USA

    Jie Gao & Dengpan Zhou

Authors
  1. Jie Gao
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  2. Dengpan Zhou
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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© 2011 Springer-Verlag Berlin Heidelberg

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Gao, J., Zhou, D. (2011). Resilient and Low Stretch Routing through Embedding into Tree Metrics. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_37

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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