The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems

TL;DR

This paper introduces the Shortlist Method, a faster algorithm for solving the Earth Mover's Distance and transportation problems, significantly reducing computation time for large-scale applications.

Contribution

The paper presents the Shortlist Method, which reduces candidate inspection and balances pivots, along with the Modified Russell's Method for initial feasible solutions.

Findings

Significant reduction in computation time compared to traditional methods.

Effective for large-scale transportation problems.

Improved initialization and pivot strategies enhance performance.

Abstract

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.