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

PDF
Restricted to UT campus only: Request a copy
164Kb

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
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/79989
Official URL:	http://dx.doi.org/10.1007/s10107-008-0213-1
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page