Large-scale network analysis with applications to transportation, communication and inference networks
The study of large-scale networks has been mainly motivated by practical problems, like transportation and reliability problems. The problems usually involve finding optimal paths in networks and they are rather similar in nature. These different networks can be unified into a more general form of network, the semiring network. Attempts to describe such networks in a general setting is not new. \textit{D. R. Shier} [Iterative algorithms for calculating network reliability, Graph Theor. Appl. Algorithms Comput. Science, 741-752 (1975)] has described an algebraic structure to study reliability problem. \textit{B. A. Carré} [J. Inst. Math. Appl. 7, 273-294 (1971; Zbl 0219.90020)] has given an excellent description of semiring networks and their properties using matrices. In this paper, we shall describe semiring networks and show how to deal with large matrices. The latter is particularly important because in large- scale networks, even computation on the computer presents some difficulties as the amount of random access memory in every computer is limited and the computation time may be long.
scientific article; zbMATH DE number 4093205