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One of the most well-known of all network optimization problems is the shortest path problem, where a shortest connection between two locations in a road network is to be found. This problem is the basis of route planners in vehicles and on the Internet. Networks are very common structures; they consist primarily of a ?nite number of locations (points, nodes), together with a number of links (edges, arcs, connections) between the locations. Very often a certain number is attached to the links, expressing the distance or the cost between the end points of that connection. Networks occur in an extremely wide range of applications, among them are: road networks; cable networks; human relations networks; project scheduling networks; production networks; distribution networks; neural networks; networks of atoms in molecules. In all these cases there are "objects" and "relations" between the objects. A n- work optimization problem is actually nothing else than the problem of ?nding a subset of the objects and the relations, such that a certain optimization objective is satis?ed.
List of contents
The Modeling and Implementing Process.- Network Theory.- References with Comments.- Shortest Paths.- Minimum Spanning Trees.- Network Flows.- Matchings.- Facility Location.- Cyclic Routing on Networks.- Erratum.
Summary
One of the most well-known of all network optimization problems is the shortest path problem, where a shortest connection between two locations in a road network is to be found. This problem is the basis of route planners in vehicles and on the Internet. Networks are very common structures; they consist primarily of a ?nite number of locations (points, nodes), together with a number of links (edges, arcs, connections) between the locations. Very often a certain number is attached to the links, expressing the distance or the cost between the end points of that connection. Networks occur in an extremely wide range of applications, among them are: road networks; cable networks; human relations networks; project scheduling networks; production networks; distribution networks; neural networks; networks of atoms in molecules. In all these cases there are “objects” and “relations” between the objects. A n- work optimization problem is actually nothing else than the problem of ?nding a subset of the objects and the relations, such that a certain optimization objective is satis?ed.
Additional text
From the reviews:
“The book presents in a very interesting way different problems connected with network optimization. … I would strongly recommend the book as a complementary material for a graduate course on network optimization or related subjects.” (Jacek Błazewicz, Zentralblatt MATH, Vol. 1217, 2011)
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From the reviews:
"The book presents in a very interesting way different problems connected with network optimization. ... I would strongly recommend the book as a complementary material for a graduate course on network optimization or related subjects." (Jacek Blazewicz, Zentralblatt MATH, Vol. 1217, 2011)
