LIPIcs.ESA.2024.52.pdf
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Toward Self-Adjusting k-Ary Search Tree Networks
Authors
Anton Paramonov 
,
Iosif Salem ,
Vitaly Aksenov ,
Stefan Schmid
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32nd Annual European Symposium on Algorithms (ESA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-23
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Evgeniy Feder, Anton Paramonov, Pavel Mavrin, Iosif Salem, Vitaly Aksenov, and Stefan Schmid. Toward Self-Adjusting k-Ary Search Tree Networks. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.52
https://doi.org/10.4230/LIPIcs.ESA.2024.52
Abstract
Datacenter networks are becoming increasingly flexible with the incorporation of new optical communication technologies, such as optical circuit switches, enabling self-adjusting topologies that can adapt to the traffic pattern in a demand-aware manner. In this paper, we take the first steps toward demand-aware and self-adjusting k-ary tree networks. These are more powerful generalizations of existing binary search tree networks (like SplayNet [Stefan Schmid et al., 2016]), which have been at the core of self-adjusting network (SAN) designs. k-ary search tree networks are a natural generalization offering nodes of higher degrees, reduced route lengths, and local routing in spite of reconfigurations (due to maintaining the search property).
Our main results are two online heuristics for self-adjusting k-ary tree networks. Empirical results show that our heuristics work better than SplayNet in most of the real network traces and for average to low locality synthetic traces, and are only a little inferior to SplayNet in all remaining traces. We build our online algorithms by first solving the offline case. First, we compute an offline (optimal) static demand-aware network for arbitrary traffic patterns in 𝒪(n³ ⋅ k) time via dynamic programming, where n is the number of network nodes (e.g., datacenter racks), and also improve the bound for the special case of uniformly distributed traffic. Then, we present a centroid-based approach to demand-aware network designs that we use both in the offline static and online settings. In the offline uniform-workload case, we construct this centroid network in linear time 𝒪(n).
Subject Classification
ACM Subject Classification
- Networks → Network algorithms
- Networks → Network design principles
- Theory of computation → Online algorithms
- Theory of computation → Data structures design and analysis
Keywords
- self-adjusting networks
- networks
- splay-tree
- k-ary tree
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References
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