Result: Covering a set of points with a minimum number of lines
Title:
Covering a set of points with a minimum number of lines
Authors:
Source:
Algorithms and complexity (6th Italian conference, CIAC 2006, Rome, Italy, May 29-31, 2006)0CIAC 2006. :6-17
Publisher Information:
Berlin: Springer, 2006.
Publication Year:
2006
Physical Description:
print, 9 ref 1
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Algorithme, Algorithm, Algoritmo, Borne inférieure, Lower bound, Cota inferior, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Complexité calcul, Computational complexity, Complejidad computación, Complexité temps, Time complexity, Complejidad tiempo, Couverture, Coverage, Cobertura, Problème recouvrement, Covering problem, Problema recubrimiento, Recouvrement ensemble, Set covering, Cubierta conjunto, Structure arborescente, Tree structure, Estructura arborescente
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Science, Lund University, Box 118, 221 Lund, Sweden
ISSN:
0302-9743
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.19150294
Database:
PASCAL Archive
Further Information
We consider the minimum line covering problem: given a set S of n points in the plane, we want to find the smallest number l of straight lines needed to cover all n points in S. We show that this problem can be solved in O(n log l) time if I ∈ O(log1-e n), and that this is optimal in the algebraic computation tree model (we show that the Ω(nlogl) lower bound holds for all values of I up to O(√n)). Furthermore, a O(log l)-factor approximation can be found within the same O(nlogl) time bound if l ∈ O(4√n). For the case when l ∈ Ω(logn) we suggest how to improve the time complexity of the exact algorithm by a factor exponential in l.