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Brief Announcement

DOI: 10.4230/LIPIcs.DISC.2025.52

Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication

Authors: Andrei Constantinescu, Marc Dufay, Anton Paramonov, and Roger Wattenhofer

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

We study the problem of Strong Byzantine Agreement and establish tight upper and lower bounds on communication complexity, parameterized by the actual number of Byzantine faults. Specifically, for a system of n parties tolerating up to t Byzantine faults, out of which only f ≤ t are actually faulty, we obtain the following results: In the partially synchronous setting, we present the first Byzantine Agreement protocol that achieves adaptive communication complexity of 𝒪(n + t ⋅ f) words, which is asymptotically optimal. Our protocol has an optimal resilience of t < n/3. In the asynchronous setting, we prove a lower bound of Ω(n + t²) on the expected number of messages, and design an almost matching protocol with an optimal resilience that solves agreement with 𝒪((n + t²)⋅ log n) words. Our main technical contribution in the asynchronous setting is the utilization of a bipartite expander graph that allows for low-cost information dissemination.

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Andrei Constantinescu, Marc Dufay, Anton Paramonov, and Roger Wattenhofer. Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 52:1-52:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{constantinescu_et_al:LIPIcs.DISC.2025.52,
  author =	{Constantinescu, Andrei and Dufay, Marc and Paramonov, Anton and Wattenhofer, Roger},
  title =	{{Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{52:1--52:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.52},
  URN =		{urn:nbn:de:0030-drops-248680},
  doi =		{10.4230/LIPIcs.DISC.2025.52},
  annote =	{Keywords: Byzantine Agreement, Communication Complexity, Adaptive Communication Complexity, Resilience}
}

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DOI: 10.4230/LIPIcs.ESA.2024.52

Toward Self-Adjusting k-Ary Search Tree Networks

Authors: Evgeniy Feder, Anton Paramonov, Pavel Mavrin, Iosif Salem, Vitaly Aksenov, and Stefan Schmid

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

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).

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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)

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@InProceedings{feder_et_al:LIPIcs.ESA.2024.52,
  author =	{Feder, Evgeniy and Paramonov, Anton and Mavrin, Pavel and Salem, Iosif and Aksenov, Vitaly and Schmid, Stefan},
  title =	{{Toward Self-Adjusting k-Ary Search Tree Networks}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{52:1--52:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.52},
  URN =		{urn:nbn:de:0030-drops-211235},
  doi =		{10.4230/LIPIcs.ESA.2024.52},
  annote =	{Keywords: self-adjusting networks, networks, splay-tree, k-ary tree}
}

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Documents authored by Paramonov, Anton

Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication

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Toward Self-Adjusting k-Ary Search Tree Networks

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