2026-07-26T04:14:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14826 2024-03-06T10:54:57Z ddc:004 open_access

General CONGEST Compilers against Adversarial Edges Hitron, Yael Parter, Merav CONGEST Cycle Covers Byzantine Adversaries We consider the adversarial CONGEST model of distributed computing in which a fixed number of edges (or nodes) in the graph are controlled by a computationally unbounded adversary that corrupts the computation by sending malicious messages over these (a-priori unknown) controlled edges. As in the standard CONGEST model, communication is synchronous, where per round each processor can send O(log n) bits to each of its neighbors. This paper is concerned with distributed algorithms that are both time efficient (in terms of the number of rounds), as well as, robust against a fixed number of adversarial edges. Unfortunately, the existing algorithms in this setting usually assume that the communication graph is complete (n-clique), and very little is known for graphs with arbitrary topologies. We fill in this gap by extending the methodology of [Parter and Yogev, SODA 2019] and provide a compiler that simulates any CONGEST algorithm 𝒜 (in the reliable setting) into an equivalent algorithm 𝒜' in the adversarial CONGEST model. Specifically, we show the following for every (2f+1) edge-connected graph of diameter D: - For f = 1, there is a general compiler against a single adversarial edge with a compilation overhead of Ô(D³) rounds. This improves upon the Ô(D⁵) round overhead of [Parter and Yogev, SODA 2019] and omits their assumption regarding a fault-free preprocessing phase. - For any constant f, there is a general compiler against f adversarial edges with a compilation overhead of Ô(D^{O(f)}) rounds. The prior compilers of [Parter and Yogev, SODA 2019] were limited to a single adversarial edge. Our compilers are based on a new notion of fault-tolerant cycle covers. The computation of these cycles in the adversarial CONGEST model constitutes the key technical contribution of the paper. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yael Hitron and Merav Parter 2021 Is Part Of LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2021.24 urn:nbn:de:0030-drops-148266 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.24 eng https://creativecommons.org/licenses/by/4.0/legalcode