Clarkson's Algorithm for Violator Spaces

Clarkson's algorithm is a two-staged randomized algorithm for solving linear programs, but it can also be applied to the more general LP-type problems which comprise a number of non-linear geometric problems. In 2006, it has been shown that the algorithm in its original form works for violator spaces too, which are a proper generalization of LP-type problems. In this paper we show the following theoretical results: (a) It is shown, for the first time, that Clarkson's second stage can be simplified. (b) The previous simplifications of Clarkson's first stage carry over to the violator space setting. (c) Furthermore, we show the equivalence of violator spaces and partitions of the hypercube by hypercubes.

• Type: Conference
• Year: 2009
• Where: CCCG
• Authors: Yves Brise, Bernd Gärtner
• Keywords: CCCG 2007, CCCG 2009, LP-type Problems, Two-staged Randomized Algorithm, Violator Spaces