Optimization over k-set Polytopes and Efficient k-set Enumeration

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)


We present two versions of an algorithm based on the reverse search technique for enumerating all k-sets of a point set in ℝ d . The key elements include the notion of a k-set polytope and the optimization of a linear function over a k-set polytope. In addition, we obtain several results related to the k-set polytopes. Among others, we show that the 1-skeleton of a k-set polytope restricted to vertices corresponding to the affine k-sets is not always connected.


Voronoi Diagram Unique Path Total Time Complexity Reverse Search Linear Inequality System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceETH ZürichZürichSwitzerland
  2. 2.Institute for Operations ResearchETH ZürichZürichSwitzerland

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