English

Approximate Distance Oracles for Planar Graphs with Improved Query Time-Space Tradeoff

Data Structures and Algorithms 2016-01-06 v1

Abstract

We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed epsilon > 0, we present a (1+epsilon)-approximate distance oracle with O(n(loglog n)^2) space and O((loglog n)^3) query time. This improves the previous best product of query time and space of the oracles of Thorup (FOCS 2001, J. ACM 2004) and Klein (SODA 2002) from O(n log n) to O(n(loglog n)^5).

Keywords

Cite

@article{arxiv.1601.00839,
  title  = {Approximate Distance Oracles for Planar Graphs with Improved Query Time-Space Tradeoff},
  author = {Christian Wulff-Nilsen},
  journal= {arXiv preprint arXiv:1601.00839},
  year   = {2016}
}

Comments

20 pages, 9 figures of which 2 illustrate pseudo-code. This is the SODA 2016 version but with the definition of C_i in Phase I fixed and the analysis slightly modified accordingly. The main change is in the subsection bounding query time and stretch for Phase I

R2 v1 2026-06-22T12:23:15.864Z