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Algorithms in real algebraic geometry
Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity ofExpand
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How to draw a planar graph on a grid
TLDR
Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fáry embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide an O(n) space,O(n logn) time algorithm to effect this embedding. Expand
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On the combinatorial and algebraic complexity of quantifier elimination
TLDR
In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given. Expand
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Algebras and their automorphism groups
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Radius, diameter, and minimum degree
TLDR
We give asymptotically sharp upper bounds for the maximum diameter and radius of a connected graph, a connected trangle-free graph, and a connected C 4 -free graph with n vertices. Expand
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Multidimensional Sorting
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Upper bounds for configurations and polytopes inRd
TLDR
We give a new upper bound onnd(d+1)n on the number of realizable order types of simple configurations ofn points inRd, and ofn2d2n onthe number of combinatorial types ofsimple configurations. Expand
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Semispaces of Configurations, Cell Complexes of Arrangements
On montre que l'equivalence de semi-espace est la notion appropriee pour distinguer les proprietes des configurations qui se relient a l'orientation, la separation et la convexite
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On the Combinatorial Classification of Nondegenerate Configurations in the Plane
TLDR
We classify nondegenerate plane configurations by attaching, to each such configuration of n points, a periodic sequence of permutations of {1, 2, …, n } which satisfies some simple conditions; this classification turns out to be appropriate for questions involving convexity. Expand
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