We introduce the pseudoflow algorithm for the maximum-flow problem that employs only pseudoflows and does not generate flows explicitly. The algorithm solves directly a problem equivalent to the minimum-cut problem—the maximum blocking-cut problem. Once the maximum blocking-cut solution is available, the additional complexity required to find the respective maximum-flow is O m logn . A variant ...

Parallelizing sparse simplex algorithms is one of the most challenging problems. Because of very sparse matrices and very heavy communication, the ratio of computation to communication is extremely low. It becomes necessary to carefully select parallel algorithms , partitioning patterns, and communication optimization to achieve a speedup. Two implementations on Intel hypercubes are presented i...

In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes. 

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lö...

This paper introduces a new shortest path simplex pivot rule choosing a subset of non-basic arcs to simultaneously enter into the basis. The term multiple pivot for this operation is used. From this concept, a generic shortest path simplex algorithm with multiple pivots is described. In addition, a simplex multiple pivot rule is provided to design a shortest path simplex algorithm requiring O(n...

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007...

In this paper, we study the primal and dual simplex algorithms for the maximum flow problem. We show that aVny primal simplex algorithm for the maximum flow problem can be converted into a dual simplex algorithm that performs the same number of pivots and runs in the same time. The converse result is also true though in a somewhat weaker form.