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.

引用

页数：38

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