We consider the solution of matching problems with a convex cost function via a network flow algorithm. We review the general mapping between matching problems and flow problems on skew symmetric networks and revisit several results on optimality of network flows. We use these results to derive a balanced capacity scaling algorithm for matching problems with a linear cost function. The latter i...

This article considers a two-player strategic game for network routing under link disruptions. Player 1 (defender) routes flow through a network to maximize her value of effective flow while facing transportation costs. Player 2 (attacker) simultaneously disrupts one or more links to maximize her value of lost flow but also faces cost of disrupting links. Linear programming duality in zero-sum ...

In the minimization of the number of subtours made by an SMD placement machine the following variant of the minimum cost flow problem arised: in a network with n vertices and m arcs a set F of arcs (parametrized arcs) is given and the cost of the flow is equal to the maximum of flow values along the arcs from F . This problem can be solved by a sequence of maximum flow computations in modified ...

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...

In this paper, we consider the inverse spanning tree problem. Given an undi0 Ž 0 0 . rected graph G s N , A with n nodes, m arcs, an arc cost vector c, and a spanning tree T 0, the inverse spanning tree problem is to perturb the arc cost vector c to a vector d so that T 0 is a minimum spanning tree with respect to the < < < < cost vector d and the cost of perturbation given by d y c s Ý d y c i...

This paper presents a new strongly polynomial cut canceling algorithm for minimum cost submodular flow. The algorithm is a generalization of our similar cut canceling algorithm for ordinary min-cost flow. The algorithm scales a relaxed optimality parameter, and creates a second, inner relaxation that is a kind of submodular max flow problem. The outer relaxation uses a novel technique for relax...

In this paper the multi terminal q-FlowLoc problem (q-MT-FlowLoc) is introduced. FlowLoc problems combine two well-known modeling tools: (dynamic) network flows and locational analysis. Since the q-MT-FlowLoc problem is NP-hard we give a mixed integer programming formulation and propose a heuristic which obtains a feasible solution by calculating a maximum flow in a special graph H. If this flo...

Given an instance of the minimum cost flow problem, the corresponding inverse problem is to modify the arc costs as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. In this article, we study this inverse problem in that the modifications are measured by the weighted bottleneck-type Hamming distance. We present a new efficient algorithm ...

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...

This article considers the problems of maximum flow and minimum cost flow determining in fuzzy network. Parameters of fuzzy networks are fuzzy arc capacities in the case of maximum flow finding and transmission costs of one flow unit in the case of minimum cost flow finding. These parameters are represented as fuzzy triangular numbers. Conventional rules of operating with fuzzy triangular numbe...