Covering a set of points with a minimum number of lines

Summary, in English

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 l is an element of O(log(1-is an element of) n), and that this is optimal in the algebraic computation tree model (we show that the Omega(n log l) lower bound holds for all values of l up to O(root n)). Furthermore, a O(log l)-factor approximation can be found within the same O(n log I) time bound if l is an element of O((4)root n). For the case when l is an element of Omega(log n) we suggest how to improve the time complexity of the exact algorithm by a factor exponential in l.

• Författare: Magdalene Grantson Borgelt; Christos Levcopoulos
• Avdelning/ar: Computer Science
• Publiceringsår: 2006
• Språk: Engelska
• Sidor: 6-17
• Publikation/Tidskrift/Serie: Lecture Notes in Computer Science (Algorithms and Complexity. Proceedings)
• Volym: 3998
• Länkar: http://dx.doi.org/10.1007/11758471
• Dokumenttyp: Konferensbidrag
• Förlag: Springer
• Ämne: Computer Science
• Conference name: 6th Italian Conference, CIAC 2006
• Conference date: 2006-05-29 - 2006-05-31
• Conference place: Rome, Italy
• Status: Published
• Projekt: VR 2005-4085
• ISBN/ISSN/Övrigt: ISSN: 0302-9743; ISSN: 1611-3349; ISBN: 978-3-540-34375-2