In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The result is a min-cost flow problem in a related planar network whose balance constraints are defined by the costs of the original problem and whose costs are ...

In this paper we propose a general methodology for the optimal automatic routing of spatial pipelines motivated by recent collaboration with Ghenova, leading Naval Engineering company. We provide minimum cost multicommodity network flow based model problem incorporating all technical requirements feasible pipeline routing. A branch-and-cut approach is designed and different matheuristic algorit...

1. The average cost of a directed cycle is AvgCost(C) = ω(C) /t = e∈C ω(e) /t. (v) denote the minimum length of a walk with exactly k edges, ending at v. So, for each v, we have d 0 (v) = 0 and d k+1 (v) = min e=(u→v)∈E d k (u) + ω(e) .

The dynamic maximum flow problem that generalizes the static maximum flow problem is formulated and studied. We consider the problem on a network with capacities depending on time, fixed transit times on the arcs, and a given time horizon. The corresponding algorithm to solve this problem is proposed and some details concerning its complexity are discussed. Mathematics Subject Classification 20...

We consider the capacitated minimum cost flow problem on directed hypergraphs. We define spanning hypertrees so generalizing the spanning tree of a standard graph, and show that, like in the standard and in the generalized minimum cost flow problems, a correspondence exists between bases and spanning hypertrees. Then, we show that, like for the network simplex algorithms for the standard and fo...

Abstract. We address the two-commodity maximum flow problem on undirected networks. As a result of a change of variables, we introduce a new formulation that solves the problem through classical maximum flow techniques with only one-commodity. Therefore, a general strategy, based on this change of variables, is defined to deal with other undirected multi-commodity problems. Finally, we extend t...

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.

We consider the information theoretical capacity of the network flow watermarking problem. Finding capacity bounds of the watermarking problem can lead to compare different watermarking schemes and help in designing more efficient network flow watermarks.