On pairs of complementary GJ pivoting transforming skew-symmetric matrices

TL;DR

This paper investigates ratios related to pairs of complementary Gauss-Jordan pivotings on skew-symmetric matrices, proving a key claim that enables a more efficient implementation of a strongly polynomial-time LP algorithm.

Contribution

It proves a crucial claim involving pivoting ratios on skew-symmetric matrices, facilitating a compact implementation of a strongly polynomial LP algorithm.

Findings

Proves a key claim about pivoting ratios on skew-symmetric matrices.

Enables a more efficient implementation of a strongly polynomial LP algorithm.

Provides theoretical foundations for pivoting transformations in skew-symmetric matrices.

Abstract

This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently proposed strongly polynomial-time algorithm for the general LP problem. That Claim is proved in this article and, as a consequence of this proof, a compact implementation of the strongly polynomial-time algorithm is suggested.