TY - GEN
T1 - Vertex Fault-Tolerant Emulators
AU - Bodwin, Greg
AU - Dinitz, Michael
AU - Nazari, Yasamin
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85123978091&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ITCS.2022.25
DO - 10.4230/LIPIcs.ITCS.2022.25
M3 - Conference contribution
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 13th Innovations in Theoretical Computer Science Conference, ITCS 2022
A2 - Braverman, M.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 13th Innovations in Theoretical Computer Science Conference, ITCS 2022
Y2 - 31 January 2022 through 3 February 2022
ER -