Additive Spanner Lower Bounds with Optimal Inner Graph Structure
arxiv(2024)
摘要
We construct n-node graphs on which any O(n)-size spanner has additive
error at least +Ω(n^3/17), improving on the previous best lower bound
of Ω(n^1/7) [Bodwin-Hoppenworth FOCS '22]. Our construction completes
the first two steps of a particular three-step research program, introduced in
prior work and overviewed here, aimed at producing tight bounds for the problem
by aligning aspects of the upper and lower bound constructions. More
specifically, we develop techniques that enable the use of inner graphs in the
lower bound framework whose technical properties are provably tight with the
corresponding assumptions made in the upper bounds. As an additional
application of our techniques, we improve the corresponding lower bound for
O(n)-size additive emulators to +Ω(n^1/14).
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要