# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Tight time bounds for the minimum local convex partition problem

(2004) In Discrete and Computational Geometry. Japanese Conference, JCDCG 2004. Revised Selected Papers / Lecture Notes in Computer Science) 3742. p.95-105
Abstract
Let v be a vertex with n edges incident to it, such that the n edges partition an infinitesimally small circle C around v into convex pieces. The minimum local convex partition (MLCP) problem asks for two or three out of the n edges that still partition C into convex pieces and that are of minimum total length. We present an optimal algorithm solving the problem in linear time if the edges incident to v are sorted clockwise by angle. For unsorted edges our algorithm runs in O(n log n) time. For unsorted edges we also give a linear time approximation algorithm and a lower time bound
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
linear time approximation algorithm, lower time bound, optimal algorithm, edge partition, minimum local convex partition problem, unsorted edges, tight time bound
in
Discrete and Computational Geometry. Japanese Conference, JCDCG 2004. Revised Selected Papers / Lecture Notes in Computer Science)
volume
3742
pages
95 - 105
publisher
Springer
external identifiers
• scopus:33646529193
ISBN
3-540-30467-3
DOI
10.1007/11589440_10
project
VR 2002-4049
language
English
LU publication?
yes
id
2007-11-26 18:53:36
date last changed
2018-01-07 10:46:28
```@inbook{62bdf588-c9be-4d80-a4dc-aad7d66a43ca,
abstract     = {Let v be a vertex with n edges incident to it, such that the n edges partition an infinitesimally small circle C around v into convex pieces. The minimum local convex partition (MLCP) problem asks for two or three out of the n edges that still partition C into convex pieces and that are of minimum total length. We present an optimal algorithm solving the problem in linear time if the edges incident to v are sorted clockwise by angle. For unsorted edges our algorithm runs in O(n log n) time. For unsorted edges we also give a linear time approximation algorithm and a lower time bound},
author       = {Grantson Borgelt, Magdalene and Levcopoulos, Christos},
isbn         = {3-540-30467-3},
keyword      = {linear time approximation algorithm,lower time bound,optimal algorithm,edge partition,minimum local convex partition problem,unsorted edges,tight time bound},
language     = {eng},
pages        = {95--105},
publisher    = {Springer},
series       = {Discrete and Computational Geometry. Japanese Conference, JCDCG 2004. Revised Selected Papers / Lecture Notes in Computer Science)},
title        = {Tight time bounds for the minimum local convex partition problem},
url          = {http://dx.doi.org/10.1007/11589440_10},
volume       = {3742},
year         = {2004},
}

```