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 …

Although Random Testing (RT) is low cost and straightforward, its effectiveness is not
satisfactory. To increase the effectiveness of RT, researchers have developed Adaptive …

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 …

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 …

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 …

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 …

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 …

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 …

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)) …

We consider the problem of computing exact sums of squares (SOS) decompositions for
certain classes of non-negative multivariate polynomials, relying on semidefinite …