Girth of a Planar Digraph with Real Edge Weights in O(nlog3n) Time.

Christian Wulff-Nilsen

Girth of a Planar Digraph with Real Edge Weights in O(nlog³n) Time.

Datalogisk Institut

Abstract

The girth of a graph is the length of its shortest cycle. We give an algorithm that computes in O(n(log n)^3) time and O(n) space the (weighted) girth of an n-vertex planar digraph with arbitrary real edge weights. This is an improvement of a previous time bound of O(n^(3/2)), a bound which was only valid for non-negative edge-weights. Our algorithm can be modified to output a shortest cycle within the same time and space bounds if such a cycle exists.

Originalsprog	Engelsk
Sider	1-8
Antal sider	8
Status	Udgivet - 2009

Adgang til dokumentet

http://arxiv.org/abs/0908.0697v1

Citationsformater

@techreport{80140df023cd11df8ed1000ea68e967b,

title = "Girth of a Planar Digraph with Real Edge Weights in O(nlog3n) Time.",

abstract = "The girth of a graph is the length of its shortest cycle. We give an algorithm that computes in O(n(log n)^3) time and O(n) space the (weighted) girth of an n-vertex planar digraph with arbitrary real edge weights. This is an improvement of a previous time bound of O(n^(3/2)), a bound which was only valid for non-negative edge-weights. Our algorithm can be modified to output a shortest cycle within the same time and space bounds if such a cycle exists.",

author = "Christian Wulff-Nilsen",

year = "2009",

language = "English",

pages = "1--8",

type = "WorkingPaper",

}

TY - UNPB

T1 - Girth of a Planar Digraph with Real Edge Weights in O(nlog3n) Time.

AU - Wulff-Nilsen, Christian

PY - 2009

Y1 - 2009

N2 - The girth of a graph is the length of its shortest cycle. We give an algorithm that computes in O(n(log n)^3) time and O(n) space the (weighted) girth of an n-vertex planar digraph with arbitrary real edge weights. This is an improvement of a previous time bound of O(n^(3/2)), a bound which was only valid for non-negative edge-weights. Our algorithm can be modified to output a shortest cycle within the same time and space bounds if such a cycle exists.

AB - The girth of a graph is the length of its shortest cycle. We give an algorithm that computes in O(n(log n)^3) time and O(n) space the (weighted) girth of an n-vertex planar digraph with arbitrary real edge weights. This is an improvement of a previous time bound of O(n^(3/2)), a bound which was only valid for non-negative edge-weights. Our algorithm can be modified to output a shortest cycle within the same time and space bounds if such a cycle exists.

M3 - Working paper

SP - 1

EP - 8

BT - Girth of a Planar Digraph with Real Edge Weights in O(nlog3n) Time.

ER -