Faster Construction of Overlay Networks
Conference paper
First Online:
Abstract
We consider the problem of transforming any weakly connected overlay network of polylogarithmic degree into a topology of logarithmic diameter. The overlay network is modeled as a directed graph, in which messages are sent in synchronous rounds, and new edges can be established by sending node identifiers. However, every node can only send and receive a polylogarithmic number of bits in each round, which makes the naive approach of introducing all neighbors to each other until the network forms a clique infeasible. We present an algorithm that takes time \(O(\log ^{3/2} n)\), w.h.p. At the heart of our algorithm lies a deterministic strategy to group and merge large components of nodes, but we make use of randomized load-balancing techniques to keep the communication load of each node low. To the best of our knowledge, this is the first algorithm to improve upon the algorithm by Angluin et al. [SPAA 2005], which solves the problem in time \(O(\log ^2 n)\), and comes closer to the \(\varOmega (\log n)\) lower bound.
Keywords
Overlay networks Peer-to-peer Pointer jumpingReferences
- 1.Angluin, D., Aspnes, J., Chen, J., Wu, Y., Yin, Y.: Fast construction of overlay networks. In: Proceedings of the 17th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 145–154 (2005)Google Scholar
- 2.Aspnes, J., Shah, G.: Skip graphs. In: Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 384–393 (2003)Google Scholar
- 3.Aspnes, J., Wu, Y.: O(logn)-time overlay network construction from graphs with out-degree 1. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 286–300. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77096-1_21CrossRefGoogle Scholar
- 4.Augustine, J., et al.: Distributed computation in node-capacitated networks. In: Proceedings of the 31st Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) (2019, to appear). http://arxiv.org/abs/1805.07294
- 5.Augustine, J., Pandurangan, G., Robinson, P., Roche, S.T., Upfal, E.: Enabling robust and efficient distributed computation in dynamic peer-to-peer networks. In: Proceedings of 56th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 350–369 (2015)Google Scholar
- 6.Augustine, J., Sivasubramaniam, S.: Spartan: a framework for sparse robust addressable networks. In: Proceedings of the 32nd IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 1060–1069 (2018)Google Scholar
- 7.Barenboim, L., Elkin, M., Pettie, S., Schneider, J.: The locality of distributed symmetry breaking. J. ACM 63(3), 20:1–20:45 (2016)MathSciNetCrossRefGoogle Scholar
- 8.Berns, A., Ghosh, S., Pemmaraju, S.V.: Building self-stabilizing overlay networks with the transitive closure framework. Theor. Comput. Sci. 512, 2–14 (2013)MathSciNetCrossRefGoogle Scholar
- 9.Feldmann, M., Scheideler, C.: A self-stabilizing general De Bruijn graph. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 250–264. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69084-1_17CrossRefGoogle Scholar
- 10.Feldotto, M., Scheideler, C., Graffi, K.: HSkip+: a self-stabilizing overlay network for nodes with heterogeneous bandwidths. In: Proceedings of the 14th IEEE International Conference on Peer-to-Peer Computing (P2P), pp. 1–10 (2014)Google Scholar
- 11.Gmyr, R., Hinnenthal, K., Scheideler, C., Sohler, C.: Distributed monitoring of network properties: the power of hybrid networks. In: Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP), pp. 137:1–137:15 (2017)Google Scholar
- 12.Götte, T., Vijayalakshmi, V.R., Scheideler, C.: Always be two steps ahead of your enemy. In: Proceedings of the 33rd IEEE International Parallel and Distributed Processing Symposium (IPDPS) (2019, to appear)Google Scholar
- 13.Jacob, R., Richa, A.W., Scheideler, C., Schmid, S., Täubig, H.: Skip+: a self-stabilizing skip graph. J. ACM 61(6), 36:1–36:26 (2014)MathSciNetCrossRefGoogle Scholar
- 14.Jacob, R., Ritscher, S., Scheideler, C., Schmid, S.: Towards higher-dimensional topological self-stabilization: a distributed algorithm for delaunay graphs. Theor. Comput. Sci. 457, 137–148 (2012)MathSciNetCrossRefGoogle Scholar
- 15.Kniesburges, S., Koutsopoulos, A., Scheideler, C.: Re-chord: a self-stabilizing chord overlay network. In: Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 235–244 (2011)Google Scholar
- 16.Mitzenmacher, M., Upfal, E.: Probability and Computing. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
- 17.Onus, M., Richa, A., Scheideler, C.: Linearization: locally self-stabilizing sorting in graphs. In: Proceedings of the Meeting on Algorithm Engineering and Expermiments (ALENEX), pp. 99–108 (2007)Google Scholar
- 18.Richa, A., Scheideler, C., Stevens, P.: Self-stabilizing De Bruijn networks. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 416–430. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24550-3_31CrossRefGoogle Scholar
- 19.Rowstron, A., Druschel, P.: Pastry: scalable, decentralized object location, and routing for large-scale peer-to-peer systems. In: Guerraoui, R. (ed.) Middleware 2001. LNCS, vol. 2218, pp. 329–350. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45518-3_18CrossRefGoogle Scholar
- 20.Stoica, I., Morris, R.T., Karger, D.R., Kaashoek, M.F., Balakrishnan, H.: Chord: a scalable peer-to-peer lookup service for internet applications. In: Proceedings of the 2018 Conference of the ACM Special Interest Group on Data Communication (SIGCOMM), pp. 149–160 (2001)Google Scholar
Copyright information
© Springer Nature Switzerland AG 2019