Clarkson's algorithm for violator spaces
نویسندگان
چکیده
منابع مشابه
Clarkson's Algorithm for Violator Spaces
Clarkson’s algorithm is a two-staged randomized algorithm for solving linear programs. This algorithm has been simplified and adapted to fit the framework of LP-type problems. In this framework we can tackle a number of non-linear problems such as computing the smallest enclosing ball of a set of points in R. In 2006, it has been shown that the algorithm in its original form works for violator ...
متن کاملViolator spaces vs closure spaces
Violator Spaces were introduced by J. Matoušek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces ...
متن کاملViolator Spaces: Structure and Algorithms
Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson’s randomized algorithms for low-d...
متن کاملOn the Number of Violator Spaces
We estimate the number of violator spaces of given dimension d and number of constraints n. We show that the number of nondegenerate regular violator spaces is at most n d , and that the number of all violator spaces is at least of order exp(n). This is related to the question whether the class of optimization problems described by violator spaces (or LP-type problems) is more general than line...
متن کاملRandom Sampling in Computational Algebra: Helly Numbers and Violator Spaces
This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems and finding small generating sets of graded ideals. The cornerstone of our work is showing that the theory of violator s...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2011
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2010.09.003