Corpus ID: 3511670

Voronoi diagrams on planar graphs, and computing the diameter in deterministic $\tilde{O}(n^{5/3})$ time

  title={Voronoi diagrams on planar graphs, and computing the diameter in deterministic \$\tilde\{O\}(n^\{5/3\})\$ time},
  author={Pawel Gawrychowski and Haim Kaplan and S. Mozes and M. Sharir and Oren Weimann},
  journal={arXiv: Data Structures and Algorithms},
We present an explicit and efficient construction of additively weighted Voronoi diagrams on planar graphs. Let $G$ be a planar graph with $n$ vertices and $b$ sites that lie on a constant number of faces. We show how to preprocess $G$ in $\tilde O(nb^2)$ time (footnote: The $\tilde O$ notation hides polylogarithmic factors.) so that one can compute any additively weighted Voronoi diagram for these sites in $\tilde O(b)$ time. We use this construction to compute the diameter of a directed… Expand
3 Citations
The Inverse Voronoi Problem in Graphs I: Hardness
  • 1
  • PDF
Parameterized Complexity of Diameter
  • 5
  • PDF


Finding, Minimizing, and Counting Weighted Subgraphs
  • 69
  • PDF
Optimal Parameterized Algorithms for Planar Facility Location Problems Using Voronoi Diagrams
  • 81
  • PDF
Faster All-Pairs Shortest Paths via Circuit Complexity
  • R. Williams
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 2018
  • 52
  • Highly Influential
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
  • 96
  • PDF
Computing Graph Distances Parameterized by Treewidth and Diameter
  • 17
  • PDF
Holiest minimum-cost paths and flows in surface graphs
  • 11
  • PDF
Randomized incremental construction of abstract Voronoi diagrams
  • 59
Approximation and Fixed Parameter Subquadratic Algorithms for Radius and Diameter in Sparse Graphs
  • 129
  • PDF
Structured recursive separator decompositions for planar graphs in linear time
  • 52
  • PDF