2 research outputs found
Hamilton-Jacobi scaling limits of Pareto peeling in 2D
Pareto hull peeling is a discrete algorithm, generalizing convex hull
peeling, for sorting points in Euclidean space. We prove that Pareto peeling of
a random point set in two dimensions has a scaling limit described by a
first-order Hamilton-Jacobi equation and give an explicit formula for the
limiting Hamiltonian, which is both non-coercive and non-convex. This contrasts
with convex peeling, which converges to curvature flow. The proof involves
direct geometric manipulations in the same spirit as Calder (2016).Comment: 50 pages, 18 figures; v2 improves exposition and extends main theorem
to cover any norm in R^