Additive Spanner Lower Bounds with Optimal Inner Graph Structure

Authors Greg Bodwin , Gary Hoppenworth , Virginia Vassilevska Williams , Nicole Wein , Zixuan Xu



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Author Details

Greg Bodwin
  • University of Michigan, Ann Arbor, MI, USA
Gary Hoppenworth
  • University of Michigan, Ann Arbor, Mi, USA
Virginia Vassilevska Williams
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Nicole Wein
  • University of Michigan, Ann Arbor, MI, USA
Zixuan Xu
  • Massachusetts Institute of Technology, Cambridge, MA, USA

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Greg Bodwin, Gary Hoppenworth, Virginia Vassilevska Williams, Nicole Wein, and Zixuan Xu. Additive Spanner Lower Bounds with Optimal Inner Graph Structure. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.28

Abstract

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}).

Subject Classification

ACM Subject Classification
  • Theory of computation → Sparsification and spanners
Keywords
  • Additive Spanners
  • Graph Theory

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