Discrete & Computational Geometry

, Volume 19, Issue 3, pp 373–382

Improved Bounds for Planar k -Sets and Related Problems

  • T. K. Dey

DOI: 10.1007/PL00009354

Cite this article as:
Dey, T. Discrete Comput Geom (1998) 19: 373. doi:10.1007/PL00009354


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>

Copyright information

© 1998 Springer-Verlag New York Inc.

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