Abstract
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.
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