Result: Covering a set of points with a minimum number of lines

Title:
Covering a set of points with a minimum number of lines
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
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
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.