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Discrete & Computational Geometry

, Volume 19, Issue 3, pp 373–382 | Cite as

Improved Bounds for Planar k -Sets and Related Problems

  • T. K. Dey

Abstract.

We prove an O(n(k+1) 1/3 ) upper bound for planar k -sets. This is the first considerable improvement on this bound after its early solution approximately 27 years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k -levels in the arrangement of line segments, k convex polygons in the union of n lines, parametric minimum spanning trees, and parametric matroids in general. <lsiheader> <onlinepub>26 June, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>19n3p373.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader>

Keywords

Line Segment Span Tree Related Problem Minimum Span Tree Considerable Improvement 
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.

Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • T. K. Dey
    • 1
  1. 1.Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India 721302 dey@cse.iitkgp.ernet.inIN

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