TL;DR
This paper introduces vertex fault-tolerant emulators that outperform spanners in size, stretch, and fault-tolerance tradeoffs, providing new bounds and constructions for resilient network approximations.
Contribution
It establishes that vertex fault-tolerant emulators have superior size/stretch/fault-tolerance tradeoffs compared to spanners, with tight bounds and new constructions.
Findings
Fault-tolerant emulators surpass spanners in tradeoffs
Tight lower bounds for certain stretch parameters
Efficient constructions with additive error
Abstract
A -spanner of a graph is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of , and a -emulator is similar but not required to be a subgraph of . A classic theorem by 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…
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Videos
Vertex Fault-Tolerant Emulators· youtube
