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

@inproceedings{Cabello2017SubquadraticAF,
  title={Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs},
  author={Sergio Cabello},
  booktitle={SODA},
  year={2017}
}
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 distance 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, unweighted planar… CONTINUE READING
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Subquadratic algorithms for the diameter and the sum of pairwise distances in planar graphs

  • S. Cabello
  • Proc. 28th ACM-SIAM Symposium on Discrete…
  • 2017
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