Towards a Unified Framework for Randomized Pivoting Algorithms in Linear Programming

Abstract

this paper we present a unified framework in which we describe two known algorithms as special simplex methods and analyse their complexities and differences. 1. Introduction A linear programming (LP) problem is to find a maximizer (or minimizer) of a linear function over a system of linear inequalities. We study LP algorithms and upper bounds for the number of elementary arithmetic operations necessary to solve LP problems; for this we assume that each operation can be performed in constant time. In particular we are interested in bounds that depend only on the size m of a basis and the size n of a nonbasis. To find an LP algorithm that is polynomial in m an