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Discrete & Computational Geometry

, Volume 30, Issue 4, pp 591–606 | Cite as

Spanning Trees Crossing Few Barriers

  • Tetsuo Asano
  • Mark de Berg
  • Otfried Cheong
  • Leonidas J. Guibas
  • Jack Snoeyink
  • Hisao Tamaki
Article

Abstract

We consider the problem of finding low-cost spanning trees for sets of $n$ points in the plane, where the cost of a spanning tree is defined as the total number of intersections of tree edges with a given set of $m$ barriers. We obtain the following results: (i) if the barriers are possibly intersecting line segments, then there is always a spanning tree of cost $O(\min(m^2,m\sqrt{n}))$; (ii) if the barriers are disjoint line segments, then there is always a spanning tree of cost $O(m)$; (iii) ] if the barriers are disjoint convex objects, then there is always a spanning tree of cost $O(n+m)$. All our bounds are worst-case optimal, up to multiplicative constants.

Keywords

Line Segment Span Tree Multiplicative Constant Convex Object Disjoint Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Japan Advanced Institute of Science and Technology, Asahidai, Tatsunokuchi, Ishikawa, 923-1292Japan
  2. 2.Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB UtrechtThe Netherlands
  3. 3.Department of Computer Science, Stanford University, Stanford, CA 94305USA
  4. 4.Department of Computer Science, University of North Carolina at Chapel Hill, NC 27599-3175USA
  5. 5.Department of Computer Science, Meiji University, Higashi-Mita, Tama-ku, Kawasaki, 214Japan

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