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Selecting the Kth largest-area convex polygon

  • Jeffrey S. Salowe
Conference paper
  • 675 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)

Abstract

The purpose of this note is to solve an open problem submitted by B. Chazelle [2]: Given a set P of n points in the Euclidean plane, select the k th largest-area convex polygon determined by subsets of P. We show that the decision problem is NP-hard by a reduction from the problem of finding the k th largest m-tuple [8] determined by m sets X1,X2,...,X m . We also show that the enumeration problem is #P-complete and exhibit a pseudo-polynomial-time algorithm for the decision problem.

Keywords

Convex Hull Convex Polygon Euclidean Plane Good Subset Enumeration Problem 
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 Berlin Heidelberg 1989

Authors and Affiliations

  • Jeffrey S. Salowe
    • 1
  1. 1.Department of Computer ScienceUniversity of VirginiaCharlottesville

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