English

Planar Reachability in Linear Space and Constant Time

Data Structures and Algorithms 2015-04-07 v2

Abstract

We show how to represent a planar digraph in linear space so that distance queries can be answered in constant time. The data structure can be constructed in linear time. This representation of reachability is thus optimal in both time and space, and has optimal construction time. The previous best solution used O(nlogn)O(n\log n) space for constant query time [Thorup FOCS'01].

Keywords

Cite

@article{arxiv.1411.5867,
  title  = {Planar Reachability in Linear Space and Constant Time},
  author = {Jacob Holm and Eva Rotenberg and Mikkel Thorup},
  journal= {arXiv preprint arXiv:1411.5867},
  year   = {2015}
}

Comments

20 pages, 5 figures, submitted to FoCS

R2 v1 2026-06-22T07:07:21.122Z