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oai:drops-oai.dagstuhl.de:15621 2024-03-06T10:55:46Z ddc:004 open_access

Vertex Fault-Tolerant Emulators Bodwin, Greg Dinitz, Michael Nazari, Yasamin Emulators Fault Tolerance Girth Conjecture A k-spanner of a graph G is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of k, and a k-emulator is similar but not required to be a subgraph of G. A classic theorem by Althöfer et al. [Disc. Comp. Geom. '93] and Thorup and Zwick [JACM '05] shows that, despite the extra flexibility available to emulators, the size/stretch tradeoffs for spanners and emulators are equivalent. Our main result is that this equivalence in tradeoffs no longer holds in the commonly-studied setting of graphs with vertex failures. That is: we introduce a natural definition of vertex fault-tolerant emulators, and then we show a three-way tradeoff between size, stretch, and fault-tolerance for these emulators that polynomially surpasses the tradeoff known to be optimal for spanners. We complement our emulator upper bound with a lower bound construction that is essentially tight (within log n factors of the upper bound) when the stretch is 2k-1 and k is either a fixed odd integer or 2. We also show constructions of fault-tolerant emulators with additive error, demonstrating that these also enjoy significantly improved tradeoffs over those available for fault-tolerant additive spanners. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Greg Bodwin and Michael Dinitz and Yasamin Nazari 2022 Is Part Of LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2022.25 urn:nbn:de:0030-drops-156217 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.25 eng https://creativecommons.org/licenses/by/4.0/legalcode