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Showing papers on "Greedy algorithm published in 1969"


Journal ArticleDOI
T. C. Raymond1
TL;DR: New heuristic algorithm that has been programmed for a digital computer and that obtains optimal or near-optimal solutions to the classical traveling-salesman problem is described.
Abstract: The classical traveling-salesman problem is to determine a tour that will minimize the total distance or cost involved in visiting several cities and returningt o the starting point. This paper describes new heuristic algorithm that has been programmed for a digital computer and that obtains optimal or near-optimal solutions to the problem. The author's general approach was derived from an existing algorithm developed by Karg and Thompson in 1964. Computational results for five multi-city tours are presented and the algorithm is shown to be competitive with other existing heuristic techniques.

37 citations


01 May 1969
TL;DR: In this paper, the authors present an extension of matroid theory so as to apply to infinite as well as finite systems, which is called matroid axiomatics and applies to two important classes of infinite matroids.
Abstract: : The notion of a matroid was introduced by H. Whitney in 1932, in order to provide a unified treatment of the dependence structures of graph theory and linear algebra. In more recent years, the same notion has served to unify other areas of combinatorial mathematics. For example, the so-called greedy algorithm for finite matroids contains, as special cases, an algorithm for finding optimal assignments (of people to jobs, for example) and an algorithm for finding the shortest spanning tree of a graph (useful in the design of communication or transportation networks for certain purposes). The present report is concerned primarily with the extension of matroid theory so as to apply to infinite as well as finite systems. It contributes to matroid axiomatics and shows that the greedy algorithm applies to two important classes of infinite matroids. (Author)

23 citations