The paper presents a new construction of an n-node graph on which any linear-sized additive spanner or emulator must have large additive error. Specifically:
For additive spanners, the authors construct a graph where any linear-sized spanner has additive error at least Ω(n^3/17), improving on the previous best lower bound of Ω(n^1/7).
For additive emulators, the authors obtain a lower bound of Ω(n^1/14), improving on the previous best lower bound of Ω(n^2/29).
The key technical innovations are:
These improvements to the lower bound framework bring the upper and lower bounds closer together, making progress towards tight bounds for additive spanners and emulators.
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by Greg Bodwin,... pada arxiv.org 04-30-2024
https://arxiv.org/pdf/2404.18337.pdfPertanyaan yang Lebih Dalam