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Distributed computations in fully-defective networks

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A Correction to this article was published on 30 September 2023

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Abstract

We address fully-defective asynchronous networks, in which all links are subject to an unlimited number of alteration errors, implying that all messages in the network may be completely corrupted. Despite the possible intuition that such a setting is too harsh for any reliable communication, we show how to simulate any algorithm for a noiseless setting over any fully-defective setting, given that the network is 2-edge connected. We prove that if the network is not 2-edge connected, no non-trivial computation in the fully-defective setting is possible. The key structural property of 2-edge-connected graphs that we leverage is the existence of an oriented (non-simple) cycle that goes through all nodes (Robbins, Am. Math. Mon., 1939). The core of our technical contribution is presenting a construction of such a Robbins cycle in fully-defective networks, and showing how to communicate over it despite total message corruption. These are obtained in a content-oblivious manner, since nodes must ignore the content of received messages.

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  1. For instance, let \(P=(a\rightarrow b\rightarrow c \rightarrow b \rightarrow e)\), then \(a {\Rightarrow }^{} e\) is the path \((a\rightarrow b\rightarrow e)\) which is not a sub-path of P.

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Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 755839. Ran Gelles is supported in part by the Israel Science Foundation (ISF) through Grant No. 1078/17 and the United States-Israel Binational Science Foundation (BSF) through Grant No. 2020277. Gal Sela is supported in part by the Israel Science Foundation (ISF) through Grant No. 1102/21.

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Authors and Affiliations

  1. Technion, Haifa, Israel

    Keren Censor-Hillel, Shir Cohen & Gal Sela

  2. Bar-Ilan University, Ramat-Gan, Israel

    Ran Gelles

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A preliminary version of this work appeared in PODC’22 [7].

The online published version of this article has been revised as the algorithm citations were incorrectly numbered and the author’s corrections for the same were missed out to be incorporated.

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Censor-Hillel, K., Cohen, S., Gelles, R. et al. Distributed computations in fully-defective networks. Distrib. Comput. 36, 501–528 (2023). https://doi.org/10.1007/s00446-023-00452-2

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