Abstract

We present a new planar convex hull algorithm with worst case time complexity $O(n\log H)$ where n is the size of the input set and H is the size of the output set, i.e. the number of vertices found to be on the hull. We also show that this algorithm is asymptotically worst case optimal on a rather realistic model of computation even if the complexity of the problem is measured in terms of input as well as output size. The algorithm relies on a variation of the divide-and-conquer paradigm which we call the “marriage-before-conquest” principle and which appears to be interesting in its own right.

MSC codes

  1. 68P10
  2. 52-04
  3. 52A10

Keywords

  1. computational geometry
  2. convex hull
  3. divide-and-conquer
  4. lower bounds

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 287 - 299
ISSN (online): 1095-7111

History

Submitted: 15 November 1983
Published online: 2 August 2006

MSC codes

  1. 68P10
  2. 52-04
  3. 52A10

Keywords

  1. computational geometry
  2. convex hull
  3. divide-and-conquer
  4. lower bounds

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