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Covering a set of points with a minimum number of lines

Publiceringsår: 2006
Språk: Engelska
Sidor: 6-17
Publikation/Tidskrift/Serie: Lecture Notes in Computer Science (Algorithms and Complexity. Proceedings)
Volym: 3998
Dokumenttyp: Konferensbidrag
Förlag: Springer


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.


  • Computer Science


6th Italian Conference, CIAC 2006
  • VR 2005-4085
  • ISSN: 1611-3349
  • ISSN: 0302-9743
  • ISBN: 978-3-540-34375-2

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