There are many depth measures on point sets that yield centerpoint theorems. These theorems guarantee the existence of points of a specified depth, a kind of geometric median. How...
The finite element (FE) mesh sizing has great influence on computational time, memory usage, and accuracy of FE analysis. Based on a systematic in-depth study of the geometric com...
William Roshan Quadros, Steven J. Owen, Michael L....
The problem of interest is covering a given point set with homothetic copies of several convex containers C1,...,Ck, while the objective is to minimize the maximum over the dilatat...
Two long-open problems have been solved: (1) every sufficiently large planar point set in general position contains the vertices of an empty hexagon; (2) every finite collection o...
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of [0, 1]n. We take this basic fact as a starting poin...