Random sampling in computational algebra: Helly numbers and violator spaces
نویسندگان
چکیده
منابع مشابه
Random 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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This paper transfers a randomized algorithm originally used in geometric optimization to computational commutative algebra. We show that Clarkson’s sampling algorithm can be applied to two separate problems in computational algebra: solving large-scale polynomial systems, for which we utilize a Helly-type result for algebraic varieties, and finding small generating sets of graded ideals. The co...
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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 ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2016
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2016.01.001