Voronoi diagrams and Delaunay triangulations
S Fortune - Handbook of discrete and computational geometry, 2017 - api.taylorfrancis.com
The Voronoi diagram of a set of sites partitions space into regions, one per site; the region
for a site s consists of all points closer to s than to any other site. The dual of the Voronoi …
for a site s consists of all points closer to s than to any other site. The dual of the Voronoi …
Centroidal voronoi tessellations-a new approach to random testing
A Shahbazi, AF Tappenden… - IEEE Transactions on …, 2012 - ieeexplore.ieee.org
Although Random Testing (RT) is low cost and straightforward, its effectiveness is not
satisfactory. To increase the effectiveness of RT, researchers have developed Adaptive …
satisfactory. To increase the effectiveness of RT, researchers have developed Adaptive …
Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
We present a hybrid symbolic-numeric algorithm for certifying a polynomial or rational
function with rational coefficients to be non-negative for all real values of the variables by …
function with rational coefficients to be non-negative for all real values of the variables by …
[PDF][PDF] State of the union (of geometric objects)
Let C be a set of geometric objects in Rd. The combinatorial complexity of the union of C is
the total number of faces of all dimensions on its boundary. We survey the known upper …
the total number of faces of all dimensions on its boundary. We survey the known upper …
Estimation of geodesic tortuosity and constrictivity in stationary random closed sets
We investigate the problem of estimating geodesic tortuosity and constrictivity as two
structural characteristics of stationary random closed sets. They are of central importance for …
structural characteristics of stationary random closed sets. They are of central importance for …
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to computing lower
bound certificates for several well-known factorization problems in hybrid symbolic-numeric …
bound certificates for several well-known factorization problems in hybrid symbolic-numeric …
Probabilistic algorithm for polynomial optimization over a real algebraic set
A Greuet, M Safey El Din - SIAM Journal on Optimization, 2014 - SIAM
Let f,f_1,...,f_s be n-variate polynomials with rational coefficients of maximum degree D and
let V be the set of common complex solutions of F=(f_1,...,f_s). We give an algorithm which …
let V be the set of common complex solutions of F=(f_1,...,f_s). We give an algorithm which …
Critical points and Gröbner bases: the unmixed case
JC Faugère, MS El Din, PJ Spaenlehauer - Proceedings of the 37th …, 2012 - dl.acm.org
We consider the problem of computing critical points of the restriction of a polynomial map to
an algebraic variety. This is of first importance since the global minimum of such a map is …
an algebraic variety. This is of first importance since the global minimum of such a map is …
Computing the global optimum of a multivariate polynomial over the reals
MS El Din - Proceedings of the twenty-first international symposium …, 2008 - dl.acm.org
Let f be a polynomial in Q [X1,..., Xn] of degree D. We provide an efficient algorithm in
practice to compute the global supremum supx∈ Rn f (x) of f (or its infimum inf {x∈ Rn} f (x)) …
practice to compute the global supremum supx∈ Rn f (x) of f (or its infimum inf {x∈ Rn} f (x)) …
On exact Reznick, Hilbert-Artin and Putinar's representations
We consider the problem of computing exact sums of squares (SOS) decompositions for
certain classes of non-negative multivariate polynomials, relying on semidefinite …
certain classes of non-negative multivariate polynomials, relying on semidefinite …