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Recent developments in the use of greedy algorithms in linear programming are reviewed and extended. We find a common generalization of some theorems of Queyranne—Spieksma— Tardella, Faigle—Kern, and Fujishige about greedy algorithms for linear programs in diverse contexts. Additionally, we extend a well-known theorem of Topkis about submodular functions on the product of chains to submodular functions on the product of lattices.
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