This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
41st Annual Symposium on Foundations of Computer Science
On the boundary complexity of the union of fat triangles
Redondo Beach, California
November 12-November 14
ISBN: 0-7695-0850-2
J. Pach, City Coll., CUNY, NY, USA
G. Tardos, City Coll., CUNY, NY, USA
A triangle is said to be /spl delta/-fat if its smallest angle is at least /spl delta/<0. A connected component of the complement of the union of a family of triangles is called hole. It is shown that any family of /spl delta/-far triangles in the plane determines at most O (n//spl delta/ log 2//spl delta/) holes. This improves on some earlier bounds of (Efrat et al., 1993; Matousek et al., 1994). Solving a problem of (Agarwal and Bern, 1999) we also give a general upper bound for the number of holes determined by n triangles in the plane with given angles. As a corollary, we obtain improved upper bounds for the boundary complexity of the union of fat polygons in the plane, which, in turn, leads to better upper bounds for the running times of some known algorithms for motion planning, for finding a separator line for a set of segments, etc.
Index Terms:
computational complexity; computational geometry; boundary complexity; fat triangle union; holes; upper bounds; motion planning; separator line; computational geometry
Citation:
J. Pach, G. Tardos, "On the boundary complexity of the union of fat triangles," focs, pp.423, 41st Annual Symposium on Foundations of Computer Science, 2000
Usage of this product signifies your acceptance of the Terms of Use.