Graph theory in operations research/ Boffey

x, 301 hal.: ill.; 26 cm

Design of electricity supply networks

AbstractThe problem of designing a secure electricity supply network at minimal cost is formulated as a mathematical program. It is also shown how computationally convenient new constraints may be derived and these are added to the original set. The problem is dualized and solved approximately. It is indicated how this approach can be built into a Branch-and-Bound scheme for solving the original design problem, and an illustrative example is given

A comprehensive survey on the quickest path problem

Abstract This work is a survey on a special minsum-maxmin bicriteria problem, known as the quickest path problem, that can model the transmission of data between two nodes of a network. Moreover, the authors review the problems of ranking the K quickest paths, and the K quickest loopless paths, and compare them in terms of the worst-case complexity order. The classification presented led to the proposal of a new variant of a known K quickest loopless paths algorithm. Finally, applications of quickest path algorithms are mentioned, as well as some comparative empirical results