Anti-matroids

Authors:
Gregory Gutin;Anders Yeo
Affiliations:
Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK
Venue:
Operations Research Letters
Year:
2002

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Abstract

We introduce an anti-matroid as a family F of subsets of a ground set E for which there exists an assignment of weights to the elements of E such that the greedy algorithm to compute a maximal set (with respect to inclusion) in F of minimum weight finds, instead, the unique maximal set of maximum weight. We introduce a special class of anti-matroids, I-anti-matroids, and show that the asymmetric and symmetric TSP as well as the assignment problem are I-anti-matroids.