Abstract
This paper introduces the problem of communication pattern adaption for a distributed self-adjusting binary search tree. We propose a simple local algorithm that is closely related to the nearly thirty-year-old idea of splay trees and evaluate its adaption performance in the distributed scenario if different communication patterns are provided. To do so, the process of self-adjustment is modeled similarly to a basic network creation game in which the nodes want to communicate with only a certain subset of all nodes. We show that, in general, the game (i.e., the process of local adjustments) does not converge, and convergence is related to certain structures of the communication interests, which we call conflicts. We classify conflicts and show that for two communication scenarios in which convergence is guaranteed, the self-adjusting tree performs well. Furthermore, we investigate the different classes of conflicts separately and show that, for a certain class of conflicts, the performance of the tree network is asymptotically as good as the performance for converging instances. However, for the other conflict classes, a distributed self-adjusting binary search tree adapts poorly.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901).
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References
Adelson-Velsky, G.M., Landis, Y.M.: An algorithm for the organization of information. Deklady Akademii Nauk USSR 16 16(2), 263–266 (1962)
Alon, N., Demaine, E.D., Hajiaghayi, M., Leighton, T.: Basic network creation games. In: SPAA, pp. 106–113 (2010)
Arora, D., Bienkowski, M., Feldmann, A., Schaffrath, G., Schmid, S.: Online strategies for intra and inter provider service migration in virtual networks. In: IPTcomm (2011)
Avin, C., Haeupler, B., Lotker, Z., Scheideler, C., Schmid, S.: Locally self-adjusting tree networks. In: IPDPS, pp. 395–406 (2013)
Bayer, R.: Symmetric binary b-trees: Data structure and maintenance algorithms. Acta Inf. 1, 290–306 (1972)
Cord-Landwehr, A., Hüllmann, M., Kling, P., Setzer, A.: Basic network creation games with communication interests. In: SAGT, pp. 72–83 (2012)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: PODC, pp. 347–351 (2003)
Galperin, I., Rivest, R.L.: Scapegoat trees. In: SODA, pp. 165–174 (1993)
Goemans, M.X., Mirrokni, V.S., Vetta, A.: Sink equilibria and convergence. In: FOCS, pp. 142–154 (2005)
Heller, B., Seetharaman, S., Mahadevan, P., Yiakoumis, Y., Sharma, P., Banerjee, S., McKeown, N.: Elastictree: Saving energy in data center networks. In: NSDI, pp. 249–264 (2010)
Leitao, J.C.A., da Silva Ferreira Moura Marques, J.P., Pereira, J.O.R.N., Rodrigues, L.E.T.: X-BOT: A protocol for resilient optimization of unstructured overlays. In: SRDS, pp. 236–245 (2009)
Lenzner, P.: On dynamics in basic network creation games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 254–265. Springer, Heidelberg (2011)
Shang, Y., Li, D., Xu, M.: Energy-aware routing in data center network. In: Green Networking, pp. 1–8 (2010)
Sherk, M.: Self-adjusting k-ary search trees. In: Dehne, F., Santoro, N., Sack, J.-R. (eds.) WADS 1989. LNCS, vol. 382, pp. 381–392. Springer, Heidelberg (1989)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary trees. In: STOC, pp. 235–245 (1983)
Tang, M., Liu, Z., Liang, X., Hui, P.M.: Self-adjusting routing schemes for time-varying traffic in scale-free networks. Phys. Rev. E 80, 026114 (2009)
Wang, C.C., Derryberry, J., Sleator, D.D.: O(log log n)-competitive dynamic binary search trees. In: SODA, pp. 374–383 (2006)
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Strothmann, T. (2015). The Impact of Communication Patterns on Distributed Self-Adjusting Binary Search Trees. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_16
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DOI: https://doi.org/10.1007/978-3-319-15612-5_16
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