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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Fault-tolerant Consensus is about reaching agreement on some of the input values in a limited time by non-faulty autonomous processes, despite of failures of processes or communication medium. This problem is particularly challenging and costly against an adaptive adversary with full information. Bar-Joseph and Ben-Or (PODC'98) were the first who proved an absolute lower bound Ω(√{n/log n}) on expected time complexity of Consensus in any classical (i.e., randomized or deterministic) message-passing network with n processes succeeding with probability 1 against such a strong adaptive adversary crashing processes.
Seminal work of Ben-Or and Hassidim (STOC'05) broke the Ω(√{n/log n}) barrier for consensus in the classical (deterministic and randomized) networks by enhancing the model with quantum channels. In such networks, quantum communication between every pair of processes participating in the protocol is also allowed. They showed an (expected) constant-time quantum algorithm for a linear number of crashes t < n/3.
In this paper, we improve upon that seminal work by reducing the number of quantum and communication bits to an arbitrarily small polynomial, and even more, to a polylogarithmic number - though, the latter in the cost of a slightly larger polylogarithmic time (still exponentially smaller than the time lower bound Ω(√{n/log n}) for the classical computation models).

Mohammad T. HajiAghayi, Dariusz R. Kowalski, and Jan Olkowski. Distributed Fast Crash-Tolerant Consensus with Nearly-Linear Quantum Communication. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 80:1-80:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hajiaghayi_et_al:LIPIcs.ICALP.2024.80, author = {HajiAghayi, Mohammad T. and Kowalski, Dariusz R. and Olkowski, Jan}, title = {{Distributed Fast Crash-Tolerant Consensus with Nearly-Linear Quantum Communication}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {80:1--80:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.80}, URN = {urn:nbn:de:0030-drops-202235}, doi = {10.4230/LIPIcs.ICALP.2024.80}, annote = {Keywords: distributed algorithms, quantum algorithms, adaptive adversary, crash failures, Consensus, quantum common coin, approximate counting} }

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**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

We study Consensus in synchronous networks with arbitrary connected topologies. Nodes may be faulty, in the sense of either Byzantine or proneness to crashing. Let t denote a known upper bound on the number of faulty nodes, and D_s denote a maximum diameter of a network obtained by removing up to s nodes, assuming the network is (s+1)-connected. We give an algorithm for Consensus running in time t + D_{2t} with nodes subject to Byzantine faults. We show that, for any algorithm solving Consensus for Byzantine nodes, there is a network G and an execution of the algorithm on this network that takes Ω(t + D_{2t}) rounds. We give an algorithm solving Consensus in t + D_{t} communication rounds with Byzantine nodes using authenticated messages of polynomial size. We show that for any numbers t and d > 4, there exists a network G and an algorithm solving Consensus with Byzantine nodes using authenticated messages in fewer than t + 3 rounds on G, but all algorithms solving Consensus without message authentication require at least t + d rounds on G. This separates Consensus with Byzantine nodes from Consensus with Byzantine nodes using message authentication, with respect to asymptotic time performance in networks of arbitrary connected topologies, which is unlike complete networks. Let f denote the number of failures actually occurring in an execution and unknown to the nodes. We develop an algorithm solving Consensus against crash failures and running in time 𝒪(f + D_{f}), assuming only that nodes know their names and can differentiate among ports; this algorithm is also communication-efficient, by using messages of size 𝒪(mlog n), where n is the number of nodes and m is the number of edges. We give a lower bound t+D_t-2 on the running time of any deterministic solution to Consensus in (t+1)-connected networks, if t nodes may crash.

Bogdan S. Chlebus, Dariusz R. Kowalski, and Jan Olkowski. Fast Agreement in Networks with Byzantine Nodes. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chlebus_et_al:LIPIcs.DISC.2020.30, author = {Chlebus, Bogdan S. and Kowalski, Dariusz R. and Olkowski, Jan}, title = {{Fast Agreement in Networks with Byzantine Nodes}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {30:1--30:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.30}, URN = {urn:nbn:de:0030-drops-131088}, doi = {10.4230/LIPIcs.DISC.2020.30}, annote = {Keywords: distributed algorithm, network, Consensus, Byzantine fault, message authentication, node crash, lower bound} }