Many Distances in Planar Graphs

被引：0
|
作者：
Sergio Cabello
机构：
[1] University of Ljubljana,Department of Mathematics, Faculty of Mathematics and Physics
[2] Institute for Mathematics,Department of Mathematics
[3] Physics and Mechanics,undefined
来源：
Algorithmica | 2012年 / 62卷
关键词：
Planar graphs; Distances in graphs; Separators; Decomposition of graphs; Data structure;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show how to compute in O(n4/3log 1/3n+n2/3k2/3log 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≤k≤n2/log 6n. As an application, we speed up previous algorithms for computing the dilation of geometric planar graphs.
引用
收藏
页码：361 / 381
页数：20
相关论文
共 50 条
  • [1] Many distances in planar graphs
    Cabello, Sergio
    [J]. PROCEEDINGS OF THE SEVENTHEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2006, : 1213 - 1220
  • [2] Many Distances in Planar Graphs
    Cabello, Sergio
    [J]. ALGORITHMICA, 2012, 62 (1-2) : 361 - 381
  • [3] DISTANCES AND CUTS IN PLANAR GRAPHS
    SCHRIJVER, A
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1989, 46 (01) : 46 - 57
  • [4] COMPUTING SHORTEST PATHS AND DISTANCES IN PLANAR GRAPHS
    DJIDJEV, HN
    PANTZIOU, GE
    ZAROLIAGIS, CD
    [J]. LECTURE NOTES IN COMPUTER SCIENCE, 1991, 510 : 327 - 338
  • [5] Fast and compact oracles for approximate distances in planar graphs
    Muller, Laurent Flindt
    Zachariasen, Martin
    [J]. ALGORITHMS - ESA 2007, PROCEEDINGS, 2007, 4698 : 657 - +
  • [6] DRAWING PLANAR GRAPHS WITH MANY COLLINEAR VERTICES
    Da Lozzo, Giordano
    Dujmovic, Vida
    Frati, Fabrizio
    Mchedlidze, Tamara
    Roselli, Vincenzo
    [J]. JOURNAL OF COMPUTATIONAL GEOMETRY, 2018, 9 (01) : 94 - 130
  • [7] Drawing Planar Graphs with Many Collinear Vertices
    Da Lozzo, Giordano
    Dujmovic, Vida
    Frati, Fabrizio
    Mchedlidze, Tamara
    Roselli, Vincenzo
    [J]. GRAPH DRAWING AND NETWORK VISUALIZATION (GD 2016), 2016, 9801 : 152 - 165
  • [8] Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs
    Cabello, Sergio
    [J]. PROCEEDINGS OF THE TWENTY-EIGHTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2017, : 2143 - 2152
  • [9] More Compact Oracles for Approximate Distances in Undirected Planar Graphs
    Kawarabayashi, Ken-ichi
    Sommer, Christian
    Thorup, Mikkel
    [J]. PROCEEDINGS OF THE TWENTY-FOURTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA 2013), 2013, : 550 - 563
  • [10] Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs
    Cabello, Sergio
    [J]. ACM TRANSACTIONS ON ALGORITHMS, 2019, 15 (02)
12345