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

被引：27
|
作者：
Cabello, Sergio [1 ,2 ]
机构：
[1] Univ Ljubljana, FMF, Dept Math, Jadranska 19, SI-1000 Ljubljana, Slovenia
[2] IMFM, Dept Math, Ljubljana, Slovenia
来源：
ACM TRANSACTIONS ON ALGORITHMS | 2019年 / 15卷 / 02期
关键词：
Planar graph; diameter; Wiener index; distances in graphs; distance counting; Voronoi diagram; SHORTEST PATHS;
D O I：
10.1145/3218821
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this article, we show how to compute for n-vertex planar graphs in O(n(11/6) 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(n(15/8) 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(n(c)) for some constant c < 2, even when restricted to undirected, unweighted planar graphs.
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页数：38
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