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# 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} }

- Published 2017 in SODA

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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