Keywords: Optimization, Linear Programming, Multiple Statistical Comparisons, Letter Displays, Computational Efficiency
Linear programming is an optimization technique commonly applied in the field of operations research to solve well-specified but computationally intensive problems. One such problem that arises in the field of computational statistics is the problem of efficiently representing the results of a large number of multiple statistical comparisons in a table or letter display. In this presentation, we present newly developed algorithms employing linear programming to find letter displays that are minimal with respect to either: a) the number of distinct letters or b) the number of total letters used by the display. We then compare these algorithms with the previously state-of-the-art algorithms for letter display production to show that minimizations based on linear programming offer a dramatic improvement in computational efficiency. In conclusion, we describe the category of problems that can be solved using linear programming, and offer guidance on how statisticians facing computationally intensive problems might leverage linear programming to increase computational efficiency.