Extended Linear Multicommodity Multicost Network And Maximal Concurent Flow Problems

Abstract

Graph is a powerful mathematical tool applied in many fields as transportation, communication, informatics, economy, … In ordinary graph the weights of edges and vertexes are considered indepently where the length of a path is the sum of weights of the edges and the vertexes on this path. However, in many practical problems, weights at a vertex are not the same for all paths passing this vertex, but depend on coming and leaving edges. In the article, a kind of weights, called switch cost, is defined. The papers study multicomodity flow problems in ordinary networks. The papers study multicomodity flow problems in extended networks, where switch costs are defined for mixed graphs. The papers develops a model of extended linear multicommodity multicost network and studies the maximal linear multicomodity multicost flow problems. The papers study the maximal multicomodity multicost flow limited cost problems. Model of extended linear multicommodity multicost network can be applied to modelize many practical problems more exactly and effectively. The presented paper studies the maximal concurent linear multicomodity multicost flow problems, that are modelized as implicit linear programming problems. On the base of dual theory in linear programming an effective aproximate algorithms is developed.

Keywords: Graph, Network, Multicommodity Multicost Flow, Optimization, Linear Programming