Self-adjusting Linear Networks
Abstract
Emerging networked systems become increasingly flexible, reconfigurable, and “self-\(*\)”. This introduces an opportunity to adjust networked systems in a demand-aware manner, leveraging spatial and temporal locality in the workload for online optimizations. However, it also introduces a tradeoff: while more frequent adjustments can improve performance, they also entail higher reconfiguration costs. This paper initiates the formal study of list networks which self-adjust to the demand in an online manner, striking a balance between the benefits and costs of reconfigurations. We show that the underlying algorithmic problem can be seen as a distributed generalization of the classic dynamic list update problem known from self-adjusting datastructures: in a network, requests can occur between node pairs. This distributed version turns out to be significantly harder than the classical problem it generalizes. Our main results are a \(\varOmega (\log {n})\) lower bound on the competitive ratio, and a (distributed) online algorithm that is \(\mathcal {O}(\log {n})\)-competitive if the communication requests are issued according to a linear order.
Keywords
Self-adjusting datastructures Competitive analysis Distributed algorithms Communication networksReferences
- 1.Albers, S.: A competitive analysis of the list update problem with lookahead. Theoret. Comput. Sci. 197(1–2), 95–109 (1998)MathSciNetCrossRefGoogle Scholar
- 2.Albers, S.: Improved randomized on-line algorithms for the list update problem. SIAM J. Comput. 27(3), 682–693 (1998)MathSciNetCrossRefGoogle Scholar
- 3.Albers, S., Von Stengel, B., Werchner, R.: A combined bit and timestamp algorithm for the list update problem. Inf. Process. Lett. 56(3), 135–139 (1995)CrossRefGoogle Scholar
- 4.Albers, S., Westbrook, J.: Self-organizing data structures. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms. LNCS, vol. 1442, pp. 13–51. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0029563CrossRefGoogle Scholar
- 5.Ambühl, C.: Offline list update is NP-hard. In: Paterson, M.S. (ed.) ESA 2000. LNCS, vol. 1879, pp. 42–51. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45253-2_5CrossRefGoogle Scholar
- 6.Avin, C., van Duijn, I., Schmid, S.: Self-adjusting linear networks. arXiv preprint arXiv:1905.02472 (2019)
- 7.Avin, C., Haeupler, B., Lotker, Z., Scheideler, C., Schmid, S.: Locally self-adjusting tree networks. In: 2013 IEEE 27th International Symposium on Parallel and Distributed Processing, pp. 395–406. IEEE (2013)Google Scholar
- 8.Avin, C., Hercules, A., Loukas, A., Schmid, S.: Towards communication-aware robust topologies. ArXiv Technical Report (2017)Google Scholar
- 9.Avin, C., Loukas, A., Pacut, M., Schmid, S.: Online balanced repartitioning. In: Gavoille, C., Ilcinkas, D. (eds.) DISC 2016. LNCS, vol. 9888, pp. 243–256. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53426-7_18CrossRefGoogle Scholar
- 10.Avin, C., Mondal, K., Schmid, S.: Demand-aware network designs of bounded degree. In: Proceedings International Symposium on Distributed Computing (DISC) (2017)Google Scholar
- 11.Avin, C., Mondal, K., Schmid, S.: Demand-aware network design with minimal congestion and route lengths. In: Proceedings of IEEE INFOCOM (2019)Google Scholar
- 12.Avin, C., Schmid, S.: Toward demand-aware networking: a theory for self-adjusting networks. In: ACM SIGCOMM Computer Communication Review (CCR) (2018)Google Scholar
- 13.Bubeck, S., Cesa-Bianchi, N., et al.: Regret analysis of stochastic and nonstochastic multi-armed bandit problems. Found. Trends® Mach. Learn. 5(1), 1–122 (2012)CrossRefGoogle Scholar
- 14.Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. (CSUR) 34(3), 313–356 (2002)CrossRefGoogle Scholar
- 15.Fenz, T., Foerster, K.T., Schmid, S., Villedieu, A.: Efficient non-segregated routing for reconfigurable demand-aware networks. In: Proceedings of IFIP Networking (2019)Google Scholar
- 16.Huq, S., Ghosh, S.: Locally self-adjusting skip graphs. In: Proceedings of IEEE 37th International Conference on Distributed Computing Systems (ICDCS), pp. 805–815 (2017)Google Scholar
- 17.Ghobadi, M., et al.: Projector: agile reconfigurable data center interconnect. In: Proceedings of ACM SIGCOMM, pp. 216–229 (2016)Google Scholar
- 18.Olver, N., Pruhs, K., Schewior, K., Sitters, R., Stougie, L.: The itinerant list update problem. In: 13th Workshop on Models and Algorithms for Planning and Scheduling Problems, p. 163 (2017)Google Scholar
- 19.Peres, B., Souza, O., Goussevskaia, O., Schmid, S., Avin, C.: Distributed self-adjusting tree networks. In: Proceedings of IEEE INFOCOM (2019)Google Scholar
- 20.Reingold, N., Westbrook, J.: Off-line algorithms for the list update problem. Inf. Process. Lett. 60(2), 75–80 (1996)MathSciNetCrossRefGoogle Scholar
- 21.Reingold, N., Westbrook, J., Sleator, D.D.: Randomized competitive algorithms for the list update problem. Algorithmica 11(1), 15–32 (1994)MathSciNetCrossRefGoogle Scholar
- 22.Schmid, S., Avin, C., Scheideler, C., Borokhovich, M., Haeupler, B., Lotker, Z.: Splaynet: towards locally self-adjusting networks. IEEE/ACM Trans. Netw. (ToN) 24, 1421–1433 (2016)CrossRefGoogle Scholar
- 23.Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar
- 24.Teia, B.: A lower bound for randomized list update algorithms. Inf. Process. Lett. 47(1), 5–9 (1993)MathSciNetCrossRefGoogle Scholar