Constant Degree Networks for Almost-Everywhere Reliable Transmission
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3717823.3718170.pdf
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749.68 KB
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5c1354dd8fce8ddc498ce3c729dc4238
Author(s)
Bafna, Mitali
Minzer, Dor
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Mitali Bafna and Dor Minzer. 2025. Constant Degree Networks for Almost-Everywhere Reliable Transmission. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 1319–1328.
Version
Final published version
Abstract
In the almost-everywhere reliable message transmission problem, introduced by [Dwork, Pippenger, Peleg, Upfal’86], the goal is to design a sparse communication network G that supports efficient, fault-tolerant protocols for interactions between all node pairs. By fault-tolerant, we mean that that even if an adversary corrupts a small fraction of vertices in G, then all but a small fraction of vertices can still communicate perfectly via the constructed protocols. Being successful to do so allows one to simulate, on a sparse graph, any fault-tolerant distributed computing task and secure multi-party computation protocols built for a complete network, with only minimal overhead in efficiency. Previous works on this problem achieved either constant-degree networks tolerating o(1) faults, constant-degree networks tolerating a constant fraction of faults via inefficient protocols (exponential work complexity), or poly-logarithmic degree networks tolerating a constant fraction of faults. We show a construction of constant-degree networks with efficient protocols (i.e., with polylogarithmic work complexity) that can tolerate a constant fraction of adversarial faults, thus solving the main open problem of Dwork et al. Our main contribution is a composition technique for communication networks, based on graph products. Our technique combines two networks tolerant to adversarial edge-faults to construct a network with a smaller degree while maintaining efficiency and fault-tolerance. We apply this composition result multiple times, using the polylogarithmic-degree edge-fault tolerant networks constructed in a recent work of [Bafna, Minzer, Vyas’24] (that are based on high-dimensional expanders) with itself, and then with the constant-degree networks (albeit with inefficient protocols) of [Upfal’92].
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3717823.3718170
