A Linear-Size Logarithmic Stretch Path-Reporting Distance Oracle for General Graphs
Michael Elkin, Seth Pettie

TL;DR
This paper introduces new compact, efficient path-reporting distance oracles for general graphs with various stretch and size tradeoffs, including linear size logarithmic stretch and near-linear query time, surpassing previous limitations.
Contribution
It presents the first path-reporting distance oracle with linear size and logarithmic stretch, along with variants achieving polylogarithmic stretch and improved query times, breaking existing conjecture thresholds.
Findings
Achieved a path-reporting oracle with size O(n^{1+1/k}) and stretch O(k).
Developed a logarithmic stretch oracle with linear size and O(n^ε) query time.
Established a tradeoff between additive stretch and size below girth conjecture thresholds.
Abstract
In 2001 Thorup and Zwick devised a distance oracle, which given an -vertex undirected graph and a parameter , has size . Upon a query their oracle constructs a -approximate path between and . The query time of the Thorup-Zwick's oracle is , and it was subsequently improved to by Chechik. A major drawback of the oracle of Thorup and Zwick is that its space is . Mendel and Naor devised an oracle with space and stretch , but their oracle can only report distance estimates and not actual paths. In this paper we devise a path-reporting distance oracle with size , stretch and query time , for an arbitrarily small . In particular, our oracle can provide logarithmic stretch using linear size. Another variant of our oracle has size $O(n…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Limits and Structures in Graph Theory
