We consider the minimum cost network flow problem min(cx : Ax=b , x > 0) on a graph G = (V,E). First we give a minor modification of Edmonds-Karp scaling technique, and we show that it solves the minimum cost flow problem in 0((|V|'^ log 1v|)(|e| + |V| log |v|)) steps. We also provide two dual simplex algorithms that solve the minimum cost flow problem in 0(|v| log |v|) pivots and 0(|v| log |v|...

Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among ot...

The constrained maximum flow problem is to send the maximum possible flow from a source node s to a sink node t in a directed network subject to a budget constraint that the cost of flow is no more than D. In this paper, we consider two versions of this problem: (i) when the cost of flow on each arc is a linear function of the amount of flow; and (ii) when the cost of flow is a convex function ...

Low Power Design has become a significant requirement when the CMOS technology entered the nanometer era. Multiple-Supply Voltage (MSV) is a popular and effective method for both dynamic and static power reduction while maintaining performance. Level shifters may cause area and Interconnect Length Overhead(ILO), and should be considered at both floorplanning and post-floorplanning stages. In th...

We present a column generation algorithm for solving the bi-objective multicommodity minimum cost flow problem. This method is based on the biobjective simplex method and Dantzig-Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using DantzigWolfe decomposition. Then, sim...

Flow in planar graphs has been extensively studied, and very efficient algorithms have been developed to compute max-flows, min-cuts, and circulations. Intimate connections between solutions to the planar circulation problem and with "consistent" potential functions in the dual graph are shown. It is also shown that the set of integral circulations in a planar graph very naturally forms a distr...

This paper presents and solves in polynomial time the minimum convex cost dynamic network flow problem, an infinite horizon integer programming problem which involves network flows evolving over time. The model is a finite network in which each arc has an associated transit time for flow to pass through it. An integral amount of flow is to be sent through arcs of the network in each period over...