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Showing papers on "Greedy algorithm published in 1973"


Journal ArticleDOI
S. Lin1, Brian W. Kernighan1
TL;DR: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems.
Abstract: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems. The procedure produces optimum solutions for all problems tested, "classical" problems appearing in the literature, as well as randomly generated test problems, up to 110 cities. Run times grow approximately as n2; in absolute terms, a typical 100-city problem requires less than 25 seconds for one case GE635, and about three minutes to obtain the optimum with above 95 per cent confidence.

3,761 citations


Journal ArticleDOI
TL;DR: This result is generalised to show that ‘greedy-type’ algorithms select an optimum forall linear functions c·x; x in some compact set U if and only if the convex closure ofU is essentially a polymatroid.
Abstract: If is a collection of subsets ofS andw is a nonnegative weight function onS, the problem of selecting a subset belonging to which has maximum weight is solved by a ‘greedy-type’ algorithm forall w if and only if is the set of independent sets of a matroid. This result is then generalised to show that ‘greedy-type’ algorithms select an optimum forall linear functionsc·x; x in some compact set $$U \subseteq R^n $$ andc > 0 if and only if the convex closure ofU is essentially a polymatroid. A byproduct of this is a new characterization of polymatroids.

62 citations


Journal ArticleDOI
TL;DR: Submittal of an algorithm for consideration for publication in Communications of the ACM implies unrestricted use of the algorithm within a computer is permissible.
Abstract: L.D. Fosdick and A.K. Cline, Editors Submittal of an algorithm for consideration for publication in Communications of the ACM implies unrestricted use of the algorithm within a computer is permissible. Copyright @ 1973, Association for Computing Machinery, Inc. General permission to republish, but not for profit, all or part of this material is granted provided that ACM's copyright notice is given and that reference is made to the publication, to its date of issue, and to the fact that reprinting privileges were granted by permission of the Association for Computing Machinery.

5 citations