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

Authors:
Artur Andrzejak;Komei Fukuda
Affiliations:
-;-
Venue:
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Year:
1999

Citing 5
Cited 2

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Computational Geometry and Graph Theory
k-sets of convex inclusion chains of planar point sets

MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science

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Abstract

We present two versions of an algorithm based on the reverse search technique for enumerating all k-sets of a point set in Rd. 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.