the existing works considering the flow-based discount factor in the hub and spoke problems, assume that increasing the amount of flow passing through each edge of network continuously decreases the unit flow transportation cost. although a higher volume of flow allows for using wider links and consequently cheaper transportation, but the unit of flow enjoys more discounts, quite like replacing...

Recently, much attention has been paid on data-driven (or swarm-like) based live streaming systems due to its rapid growth in deployment over Internet. In such systems, nodes randomly select their neighbors to form an unstructured overlay mesh (gossip-style overlay construction) and then each node requests desired data blocks from its neighbors (block scheduling). To improve the performance, mo...

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,...

This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of mini...

Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be written as a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator (MLC). We solve the problem to find an approximation B of A satisfying prescribed upper and lower bounds for each entry. The approximation B is determined such that the cor...

The present paper examines the task of minimum cost flow finding in a fuzzy dynamic network with lower flow bounds. The distinguishing feature of this problem statement lies in the fuzzy nature of the network parameters, such as flow bounds, transmission costs and transit times. The arcs of the considered network have lower bounds. Another feature of this task is that fuzzy flow bounds, costs a...

We describe a relaxation algorithm [ 1,2] for solving the classical minimum cost net-work flow problem. Our implementation is compared with mature state-of-the-artprimal simplex and primal-dual codes and is found to be several times faster on alltypes of randomly generated network flow problems. Furthermore, the speed-upfactor increases with problem dimension. The codes, called ...

This thesis presents a study of five different Lagrangian heuristics applied to the strictly convex quadratic minimum cost network flow problem. Tests are conducted on randomly generated transportation networks with different degrees of sparsity and nonlinearity according to a system devised by Ohuchi and Kaji [18]. The different heuristics performance in time and quality are compared. The unco...

Developing a polynomial time algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n 2m log nC, n2m 2 log n)) time, where n is the number of nodes in the network, m is the number of arcs, and C denotes the maximum absolute arc costs if arc costs are integer and 0 otherwise. We first introduce a pseudopo...