Optimization over k-set polytopes and efficient k-set enumeration

Abstract

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.