  Non-dominated sorting is a fundamental combinatorial problem in
multiobjective optimization, and is equivalent to the longest chain problem in
combinatorics and random growth models for crystals in materials science. In a
previous work, we showed that non-dominated sorting has a continuum limit that
corresponds to solving a Hamilton-Jacobi equation. In this work we present and
analyze a fast numerical scheme for this Hamilton-Jacobi equation, and show how
it can be used to design a fast algorithm for approximate non-dominated
sorting.
