17 citations · 18 across the 4 of their papers we have counts for
4 papers
Empty pentagons in point sets with collinearities
János Barát, Vida Dujmović, Gwenaël Joret +5
An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite s…
An upper bound on the volume of the symmetric difference of a body and a congruent copy
Daria Schymura
Let A be a bounded subset of IR^d. We give an upper bound on the volume of the symmetric difference of A and f(A) where f is a translation, a rotation, or the composition of both,…
Integer Point Sets Minimizing Average Pairwise L1-Distance: What is the Optimal Shape of a Town?
Erik D. Demaine, Sandor P. Fekete, Guenter Rote +3
An n-town, for a natural number n, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings a…
Probabilistic Matching of Planar Regions
Helmut Alt, Ludmila Scharf, Daria Schymura
We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes and , the al…