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arXiv · 1702.07815

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

Sergio Cabello
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Abstract

We show how to compute for $n$-vertex planar graphs in $O(n^{11/6}{\rm polylog}(n))$ 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 $O(n^{15/8}{\rm polylog}(n))$ 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 $O(n^c)$ for some constant $c<2$, even when restricted to undirected, unweighted planar graphs.

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Sergio Cabello. 2017-02-25. Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs. https://arxiv.org/abs/1702.07815

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