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On greedy algorithms, partially ordered sets, and submodular functions

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2 Author(s)
B. L. Dietrich ; IBM Research Division, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA ; A. J. Hoffman

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.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

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IBM Journal of Research and Development  (Volume:47 ,  Issue: 1 )