Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs

@article{Cabello2018SubquadraticAF,
  title={Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs},
  author={Sergio Cabello},
  journal={ACM Transactions on Algorithms (TALG)},
  year={2018},
  volume={15},
  pages={1 - 38}
}
  • Sergio Cabello
  • Published 2018
  • Computer Science, Mathematics
  • ACM Transactions on Algorithms (TALG)
In this article, we show how to compute for n-vertex planar graphs in O(n11/6 polylog(n)) expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In O(n15/8 polylog(n)) expected time, we can also compute the number of pairs of vertices at distances smaller than a given threshold. These are the first algorithms for these problems using time O(nc) for some constant c< 2, even when restricted to undirected… Expand
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