We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed. In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms. In this paper we show that t...

The cycle-canceling algorithm is one of the earliest algorithms to solve the minimum cost flow problem. This algorithm maintains a feasible solution x in the network G and proceeds by augmenting flows along negative cost directed cycles in the residual network G(x) and thereby canceling them. For the minimum cost flow problem with integral data, the generic version of the cycle-canceling algori...

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...

In this paper, the problem of finding the minimum cost flow line able to produce different products is considered. This problem can be formulated as a shortest path problem on an acyclic di-graph when the machines graph associated with each product family is a chain or a comb. These graphs are relevant in production planning when dealing with pipelined assembly systems. We solve the problem usi...

Earliest arrival flows capture the essence of evacuation planning. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink “as quickly as possible”. The latter requirement is made more precise by the earliest arrival property which requires that the total amount of ...

In this paper, we propose a Minimum Average-cost Path (MACP) model for segmenting 3D coronary arteries by minimizing the average edge cost along path in discrete 4D graph constructed by image voxels and associated radii. Prim's Minimum Spanning Tree method is used for efficient optimization of the MACP model. The centerline and the radii of the cross sections of the coronary artery are extracte...

Abstract. Let G = (N,A) be an undirected graph with n nodes and m arcs, a designated source node s and a sink node t. This paper addresses sensitivity analysis questions concerning the shortest s-t path (SP) problem in G and the maximum capacity s-t path (MCP) problem in G. Suppose that P* is a shortest s-t path in G with respect to a nonnegative distance vector c. For each arc e ∈ A, the lower...

The article studies the generalisation of the maximum flow of minimum cost problem for the case of maximum discrete dynamic flow of minimum travelling cost and travelling time. The approach is based on iteratively generating efficient extreme points in the objective space by solving a series of single objective maximum flow problems with different objective functions. On each of the iterations,...

We describe a Model RSM2 (A Reliable and Scalable Multicast Model). The approach we adopt uses Proactive-Routing, Minimum-Cost Path Algorithm, Combo-casting, Active Server Based Recovery, NACKBased acknowledgement, Buffer Management, Optimized Flooding Algorithm. The main characteristic of RSM2 model is, to provide complete multicasting, i.e. at the same time more than one node can act as sende...