Uniform and Monotone Line Sum Optimization

TL;DR

This paper proves that the line sum optimization problem is polynomial time solvable when restricted to uniform and monotone cases, involving matrices with specific row and column sum properties.

Contribution

It introduces polynomial algorithms for the uniform and monotone variants of the line sum optimization problem, expanding the class of efficiently solvable cases.

Findings

Polynomial time algorithms for uniform line sum optimization.

Polynomial time algorithms for monotone line sum optimization.

Identification of tractable cases within the line sum optimization problem.

Abstract

The {\em line sum optimization problem} asks for a $(0,1)$-matrix minimizing the sum of given functions evaluated at its row and column sums. We show that the {\em uniform} problem, with identical row functions and identical column functions, and the {\em monotone} problem, over matrices with nonincreasing row and column sums, are polynomial time solvable.