Titlebook: Combinatorial Optimization II; V. J. Rayward-Smith Book 1980Latest edition Springer-Verlag Berlin Heidelberg 1980 978-0-444-86040-8.algori

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Clutter percolation and random graphs,The “clutter percolation theorem” is presented and from it are deduced various results on paths in random graphs and digraphs.

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Heuristic improvement methods: How should starting solutions be chosen?,A theoretical framework for improvement heuristic methods, as applied to discrete optimization problems, is put forward. The problem of choosing a suitable set of start points, from which to perform hill-climbs, is identified and some possible solutions considered. Numerical results are presented.

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A branch and bound algorithm for the Koopmans-Beckmann quadratic assignment problem,oits both the transformation and the greedily obtained approximate solution described in a previous paper by the author. This branch and bound algorithm has the property that at each bound an associated solution is obtained simultaneously, thereby rendering any premature termination of the algorithm less wasteful.

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Optimization problems arising from the incorporation of split values in search trees,. Results are given to compare the efficiency of such trees with that of median split trees and some open problems arising are discussed. The concept of a generalised tree is introduced together with a description of how the solution of the difficult problems arising would have a considerable practical impact in the design of data bases.

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https://doi.org/10.1007/978-3-031-26204-3imum flow in this network, and minimum cuts are identified with closures for this relation. As a consequence, finding all minimum cuts reduces to a straightforward enumeration. Applications of this results arise in sensitivity and parametric analyses of networks, the vertex packing and maximum closu

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