Abstract
Self-adjusting networks (SANs) have the ability to adapt to communication demand by dynamically adjusting the workload (or demand) embedding, i.e., the mapping of communication requests into the network topology. SANs can reduce routing costs for frequently communicating node pairs by paying a cost for adjusting the embedding. This is particularly beneficial when the demand has structure, which the network can adapt to. Demand can be represented in the form of a demand graph, which is defined by the set of network nodes (vertices) and the set of pairwise communication requests (edges). Thus, adapting to the demand can be interpreted by embedding the demand graph to the network topology. This can be challenging both when the demand graph is known in advance (offline) and when it revealed edge-by-edge (online). The difficulty also depends on whether we aim at constructing a static topology or a dynamic (self-adjusting) one that improves the embedding as more parts of the demand graph are revealed. Yet very little is known about these self-adjusting embeddings.
In this paper, the network topology is restricted to a line and the demand graph to a ladder graph, i.e., a \(2\times n\) grid, including all possible subgraphs of the ladder. We present an online self-adjusting network that matches the known lower bound asymptotically and is 12-competitive in terms of request cost. As a warm up result, we present an asymptotically optimal algorithm for the cycle demand graph. We also present an oracle-based algorithm for an arbitrary demand graph that has a constant overhead.
Supported partially by the Austrian Science Fund (FWF) project I 4800-N (ADVISE) and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement No. 864228 “Self-Adjusting Networks (Adjust-Net)”.
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References
Avin, C., Bienkowski, M., Salem, I., Sama, R., Schmid, S., Schmidt, P.: Deterministic self-adjusting tree networks using rotor walks. In: 2022 IEEE 42nd International Conference on Distributed Computing Systems (ICDCS), pp. 67–77. IEEE (2022)
Avin, C., van Duijn, I., Schmid, S.: Self-adjusting linear networks. In: Ghaffari, M., Nesterenko, M., Tixeuil, S., Tucci, S., Yamauchi, Y. (eds.) SSS 2019. LNCS, vol. 11914, pp. 368–382. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34992-9_29
Avin, C., Ghobadi, M., Griner, C., Schmid, S.: On the complexity of traffic traces and implications. Proc. ACM Measur. Anal. Comput. Syst. 4(1), 1–29 (2020)
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_18
Avin, C., Mondal, K., Schmid, S.: Demand-aware network design with minimal congestion and route lengths. IEEE/ACM Trans. Netw. 30(4), 1838–1848 (2022)
Avin, C., Mondal, K., Schmid, S.: Push-down trees: optimal self-adjusting complete trees. IEEE/ACM Trans. Netw. 30(6), 2419–2432 (2022)
Avin, C., Schmid, S.: Toward demand-aware networking: a theory for self-adjusting networks. ACM SIGCOMM Comput. Commun. Rev. 48(5), 31–40 (2019)
Batista, D.M., da Fonseca, N.L.S., Granelli, F., Kliazovich, D.: Self-adjusting grid networks. In: 2007 IEEE International Conference on Communications, pp. 344–349. IEEE (2007)
Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. (CSUR) 34(3), 313–356 (2002)
Hansen, M.D.: Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems. In: 30th Annual Symposium on Foundations of Computer Science, pp. 604–609. IEEE Computer Society (1989)
Newman, I., Rabinovich, Y.: Online embedding of metrics. arXiv preprint arXiv:2303.15945 (2023)
Olver, N., Pruhs, K., Schewior, K., Sitters, R., Stougie, L.: The itinerant list update problem. In: Epstein, L., Erlebach, T. (eds.) WAOA 2018. LNCS, vol. 11312, pp. 310–326. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-04693-4_19
Paramonov, A., Salem, I., Schmid, S., Aksenov, V.: Self-adjusting linear networks with ladder demand graph. arXiv preprint arXiv:2207.03948 (2022)
Schmid, S., Avin, C., Scheideler, C., Borokhovich, M., Haeupler, B., Lotker, Z.: Splaynet: towards locally self-adjusting networks. IEEE/ACM Trans. Netw. 24(3), 1421–1433 (2016)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)
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Aksenov, V., Paramonov, A., Salem, I., Schmid, S. (2023). Self-adjusting Linear Networks with Ladder Demand Graph. In: Rajsbaum, S., Balliu, A., Daymude, J.J., Olivetti, D. (eds) Structural Information and Communication Complexity. SIROCCO 2023. Lecture Notes in Computer Science, vol 13892. Springer, Cham. https://doi.org/10.1007/978-3-031-32733-9_7
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