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Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique

Authors Keren Censor-Hillel , Orr Fischer , Ran Gelles , Pedro Soto

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  • Theory of computation → Distributed algorithms
Keywords
  • Congested Clique
  • Fault Tolerance
  • Error Correction Codes

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Abstract

We design a deterministic compiler that makes any computation in the Congested Clique model robust to a constant fraction α < 1 of adversarial crash faults. In particular, we show how a network of n nodes can compute any circuit of depth d, width ω, and gate total fan Δ, in d ⋅ ⌈ω/n² + Δ/n⌉ ⋅ 2^{O(√{log{n}}log log{n})} rounds in such a faulty model. As a corollary, any T-round Congested Clique algorithm can be compiled into an algorithm that completes in T² n^{o(1)} rounds in this model.
Our compiler obtains resilience to node crashes by coding information across the network, and its main underlying observation is that we can leverage locally-decodable codes (LDCs) to maintain a low complexity overhead, as these allow recovering the information needed at each computational step by querying only small parts of the codeword, instead of retrieving the entire coded message, which is inherent when using block codes.
The main technical contribution is that because erasures occur in known locations, which correspond to crashed nodes, we can derandomize classical LDC constructions by deterministically selecting query sets that avoid sufficiently many erasures. Moreover, when decoding multiple codewords in parallel, our derandomization load-balances the queries per-node, thereby preventing congestion and maintaining a low round complexity.
Deterministic decoding of LDCs presents a new challenge: the adversary can target precisely the (few) nodes that are queried for decoding a certain codeword. We overcome this issue via an adaptive doubling strategy: if a decoding attempt for a codeword fails, the node doubles the number of its decoding attempts. We employ a similar doubling technique when the adversary crashes the decoding node itself, replacing it dynamically with two other non-crashed nodes. By carefully combining these two doubling processes, we overcome the challenges posed by the combination of a deterministic LDC with a worst case pattern of crashes.

Cite As Get BibTex

Keren Censor-Hillel, Orr Fischer, Ran Gelles, and Pedro Soto. Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.20

Author Details

Keren Censor-Hillel
  • Technion, Haifa, Israel
Orr Fischer
  • Bar-Ilan University, Ramat Gan, Israel
Ran Gelles
  • Bar-Ilan University, Ramat Gan, Israel
Pedro Soto
  • Virginia Tech, Blacksburg, VA, USA

Funding

  • Censor-Hillel, Keren: is supported in part by the Israel Science Foundation, grant 529/23.
  • Fischer, Orr: is supported in part by the Israel Science Foundation, grant No. 1042/22 and 800/22.
  • Gelles, Ran: supported in part by the United States - Israel Binational Science Foundation (BSF), grant No. 2020277.

Acknowledgements

We would like to thank Merav Parter and Noga Ron-Zewi for helpful discussions.

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