BIT Numerical Mathematics

, Volume 32, Issue 2, pp 249–267 | Cite as

Applications of a semi-dynamic convex hull algorithm

  • John Hershberger
  • Subhash Suri
Algorithm Theory

Abstract

We obtain new results for manipulating and searching semi-dynamic planar convex hulls (subject to deletions only), and apply them to derive improved bounds for two problems in geometry and scheduling. The new convex hull results are logarithmic time bounds for set splitting and for finding a tangent when the two convex hulls are not linearly separated. Using these results, we solve the following two problems optimally inO(n logn) time: (1) [matching] givenn red points andn blue points in the plane, find a matching of red and blue points (by line segments) in which no two edges cross, and (2) [scheduling] givenn jobs with due dates, linear penalties for late completion, and a single machine on which to process them, find a schedule of jobs that minimizes the maximum penalty.

CR categories

F.2.2 I.3.5 E..1 

Additional keywords

Convex hull semi-dynamic algorithm geometric matching scheduling 

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Copyright information

© BIT Foundations 1992

Authors and Affiliations

  • John Hershberger
    • 1
    • 2
  • Subhash Suri
    • 1
    • 2
  1. 1.DEC Systems Research CenterPalo AltoUSA
  2. 2.Bell Communications ResearchMorristownUSA

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