INTERIOR METHODS FOR NONLINEAR MINIMUM COST NETWORK FLOW PROBLEMS Ryuji Katsura Japan Medical Supply Co., Ltd. Masao Fukushima Kyoto University Toshihide lbaraki Kyoto University (Received March 24,1988; Revised August 5, 1988) In this paper we propose practical algorithms for solving the nonlinear minimum cost network flow problem which has many fields of application such as production-distrib...

We address the single-source uncapacitated minimum cost network flow problem with general concave cost functions. Exact methods to solve this class of problems in their full generality are only able to address small to medium size instances, since this class of problems is known to be NP-Hard. Therefore, approximate methods are more suitable. In this work, we present a hybrid approach combining...

The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when all sources are in the first eche...

We study the task of computing a matching between two images by formulating it as an instance of the minimum-cost flow problem. Here, we use a cycle cancelling algorithm to find the optimal flow. To reduce the practical runtime, we propose a hierarchical scheme in which the images are first scaled down and then the optimal solution for the smaller problem is used as a starting point for the hig...

Let G = (V, E) be a digraph (i.e., a directed graph) with n vertices and m edges, and w : E → IR be a weight function on the edges. A directed cycle is closed walkC = (v0, v1, . . . , vt), where vt = v0 and (vi → vi+1) ∈ E, for i = 0, . . . , t − 1. The average cost of a directed cycle is AvgCost(C) = ω(C)/t = (∑e∈C ω(e)) /t. For each k = 0, 1, . . ., and v ∈ V , let dk(v) denote the minimum le...

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...

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...