A 2-Dimensional Binary Search for Integer Pareto Frontiers

TL;DR

This paper introduces an optimized 2D binary search algorithm for efficiently learning Pareto frontiers in integer grid classification problems, relevant to dynamic programming applications.

Contribution

It presents a generalized binary search method that achieves an optimal linear worst-case runtime for identifying Pareto frontiers in finite integer spaces.

Findings

Achieves worst-case runtime of (n) for the problem.

Provides a generalized binary search algorithm.

Applicable to dynamic programming contexts.

Abstract

For finite integer squares, we consider the problem of learning a classification $I$ that respects Pareto domination. The setup is natural in dynamic programming settings. We show that a generalization of the binary search algorithm achieves an optimal $\theta(n)$ worst-case run time.