Abstract
This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the benefits of such adjustments (shorter routes) and their costs (reconfigurations). In particular, we consider the problem of designing a self-adjusting tree network which serves single-source, multi-destination communication. The problem has interesting connections to self-adjusting datastructures. We present two constant-competitive online algorithms for this problem, one randomized and one deterministic. Our approach is based on a natural notion of Most Recently Used (MRU) tree, maintaining a working set. We prove that the working set is a cost lower bound for any online algorithm, and then present a randomized algorithm RANDOM-PUSH which approximates such an MRU tree at low cost, by pushing less recently used communication partners down the tree, along a random walk. Our deterministic algorithm MOVE-HALF does not directly maintain an MRU tree, but its cost is still proportional to the cost of an MRU tree, and also matches the working set lower bound.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Avin, C., Ghobadi, M., Griner, C., Schmid, S.: On the complexity of traffic traces and implications. In: Proceedings of the International Conference on Measurement and Modeling of Computer Systems, ACM SIGMETRICS, pp. 47–48 (2020)
Avin, C., Mondal, K., Schmid, S.: Demand-aware network designs of bounded degree. Distrib. Comput., 311–325 (2019). https://doi.org/10.1007/s00446-019-00351-5
Avin, C., Mondal, K., Schmid, S.: Demand-aware network design with minimal congestion and route lengths. In: Proceedings of the 38th IEEE International Conference on Computer Communications, IEEE INFOCOM, pp. 1351–1359 (2019)
Avin, C., Mondal, K., Schmid, S.: Push-down trees: optimal self-adjusting complete trees. In: Technical Report arXiv 1807.04613 (2020)
Avin, C., Schmid, S.: Toward demand-aware networking: a theory for self-adjusting networks. ACM SIGCOMM Comput. Commun. Rev. 48(5), 31–40 (2019)
Blum, A., Chawla, S., Kalai, A.: Static optimality and dynamic search-optimality in lists and trees. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2002)
Bojja Venkatakrishnan, S., Alizadeh, M., Viswanath, P.: Costly circuits, submodular schedules and approximate carathéodory theorems. In: Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science, pp. 75–88 (2016)
Bose, P., Douïeb, K., Langerman, S.: Dynamic optimality for skip lists and b-trees. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1106–1114 (2008)
Dean, B.C., Jones, Z.H.: Exploring the duality between skip lists and binary search trees. In: Proceedings of the 45th Annual Southeast Regional Conference, ACM-SE, New York, NY, USA, vol. 45, pp. 395–399. ACM (2007)
Foerster, K.T., Ghobadi, M., Schmid, S.: Characterizing the algorithmic complexity of reconfigurable data center architectures. In: Proceedings of ACM/IEEE Symposium on Architectures for Networking and Communications Systems (ANCS) (2018)
Foerster, K.T., Schmid, S.: Survey of reconfigurable data center networks: enablers, algorithms, complexity. SIGACT News 50(2), 62–79 (2019)
Fredman, M.L.: Generalizing a theorem of Wilber on rotations in binary search trees to encompass unordered binary trees. Algorithmica 62(3–4), 863–878 (2012)
Hamedazimi, N., et al.: Firefly: a reconfigurable wireless data center fabric using free-space optics. Proc. ACM SIGCOMM Comput. Commun. Rev. (CCR) 44, 319–330 (2014)
Iacono, J.: Key-independent optimality. Algorithmica 42(1), 3–10 (2005)
Kandula, S., Sengupta, S., Greenberg, A., Patel, P., Chaiken, R.: The nature of data center traffic: measurements and analysis. In: Proceedings of the 9th ACM Internet Measurement Conference (IMC), pp. 202–208 (2009)
M. Ghobadi et al.: Projector: Agile reconfigurable data center interconnect. In: Proceedings of the 2016 ACM SIGCOMM Conference, pp. 216–229 (2016)
Peres, B., Otavio, A.D.O., Goussevskaia, O., Avin, C., Schmid, S.: Distributed self-adjusting tree networks. In: Proceedings of the 38th IEEE International Conference on Computer Communications, IEEE INFOCOM, pp. 145–153 (2019)
Schmid, S., Avin, C., Scheideler, C., Borokhovich, M., Haeupler, B., Lotker, Z.: SplayNet: towards locally self-adjusting networks. IEEE/ACM Trans. Networks 24(3), 1421–1433 (2016)
Singla, A., Singh, A., Ramachandran, K., Xu, L., Zhang, Y.: Proteus: a topology malleable data center network. In: Proceedings of the 9th ACM Workshop on Hot Topics in Networks (HotNets), pp. 1–6 (2010)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)
Acknowledgments
Research supported by the ERC Consolidator grant AdjustNet (agreement no. 864228).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Avin, C., Mondal, K., Schmid, S. (2020). Dynamically Optimal Self-adjusting Single-Source Tree Networks. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-61792-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-61791-2
Online ISBN: 978-3-030-61792-9
eBook Packages: Computer ScienceComputer Science (R0)