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Many distances in planar graphs
Cabello, Sergio
We show how to compute in ▫$O(n^{4/3} \log^{1/3} n + n^{2/3}k^{2/3} \log n)$▫ time the distance between ▫$k$▫ given pairs of vertices of a planar graph ▫$G$▫ with ▫$n$▫ vertices. This improves ...previous results whenever ▫$(n/\log n)^{5/6} \le k \le n^2/\log^6 n$▫. As an application, we speed up previous algorithms for computing the dilation of geometric planar graphs.
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