- Anti-matroids Gregory Gutin (G.Gutinrhul.ac.uk) Anders Yeo (yeodaimi.au.dk) Abstract: We introduce an anti-matroid as a family $\cal F$ 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 $\cal F$ 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. Keywords: Greedy algorithm, combinatorial optimization, TSP, Category 1: Combinatorial Optimization (Approximation Algorithms ) Category 2: Combinatorial Optimization (Graphs and Matroids ) Category 3: Combinatorial Optimization (Other ) Citation: Download: [Postscript]Entry Submitted: 08/09/2001Entry Accepted: 08/09/2001Entry Last Modified: 08/09/2001Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.