A general model for matroids and the greedy algorithm


Faigle, Ulrich and Fujishige, Saturo (2009) A general model for matroids and the greedy algorithm. Mathematical programming, 119 (2). pp. 353-369. ISSN 0025-5610

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Abstract:We present a general model for set systems to be independence families with respect to set families which determine classes of proper weight functions on a ground set. Within this model, matroids arise from a natural subclass and can be characterized by the optimality of the greedy algorithm. This model includes and extends many of the models for generalized matroid-type greedy algorithms proposed in the literature and, in particular, integral polymatroids. We discuss the relationship between these general matroids and classical matroids and provide a Dilworth embedding that allows us to represent matroids with underlying partial order structures within classical matroids. Whether a similar representation is possible for matroids on convex geometries is an open question.
Item Type:Article
Copyright:© 2009 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/79989
Official URL:https://doi.org/10.1007/s10107-008-0213-1
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