On the number of simple arrangements of five double pseudolines

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.Comment: 24 pages, 16 figures, 6 table

Towards a Unified Framework for Randomized Pivoting Algorithms in Linear Programming

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