An Analysis of the Min-max Algorithm

TL;DR

This paper analyzes the min-max algorithm applied to a matrix of independent random variables, focusing on the expected number of elements read to determine the min-max value.

Contribution

It provides a theoretical calculation of the expected number of matrix elements read in the min-max algorithm for random matrices.

Findings

Derived the mean number of elements read for the min-max algorithm.

Provided analytical expressions for the expected complexity.

Enhanced understanding of the algorithm's efficiency on random data.

Abstract

We consider the matrix $A_{ij}$, whose elements are independent random variables. We calculate the mean value of the number of the elements that we need to read to find $\min_i \max_j A_{ij}$.