NDLI: An Exact Characterization of Greedy Structures

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An Exact Characterization of Greedy Structures

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Shapiro, Henry D. Helman, Paul Moret, Bernard M. E.
Copyright Year	1993
Abstract	The authors present exact characterizations of structures on which the greedy algorithm produces optimal solutions. Our characterization, which are called matroid embeddings, complete the partial characterizations of Rado [A note on independent functions, Proc. London Math. Soc., 7 (1957), pp. 300320], Gale [Optimal assignments in an ordered set, J. Combin. Theory, 4 (1968), pp. 176180], and Edmonds [Matroids and the greedy algorithm, Math. Programming, 1 (1971), pp. 127136], (matroids), and of Korte and Lovasz [Greedoids and linear object functions, SIAM J. Alg. Discrete Meth., 5 (1984), pp. 239248] and [Mathematical structures underlying greedy algorithms, in Fundamentals of Computational Theory, LNCS 177, Springer-Verlag, 1981, pp. 205209] (greedoids). It is shown that the greedy algorithm optimizes all linear objective functions if and only if the problem structure (phrased in terms of either accessible set systems or hereditary languages) is a matroid embedding. An exact characterization of the objective functions optimized by the greedy algorithm on matroid embeddings is also presented. Finally, the authors present an exact characterization of the structures on which the greedy algorithm optimizes all bottleneck functions, structures that are less constrained than matroid embeddings.
Starting Page	274
Ending Page	283
Page Count	10
File Format	PDF
ISSN	08954801
DOI	10.1137/0406021
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	6
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	1993-05-01
Access Restriction	Subscribed
Subject Keyword	linear objective function Matroids, geometric lattices set system greedoid matroid embedding greedy algorithm Combinatorics Combinatorial optimization matroid algorithmic paradigm bottleneck objective function
Content Type	Text
Resource Type	Article
Subject	Mathematics

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