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Trioid: A generalization of matroid and the associated polytope

Santosh Kabadi(kabadi***at***unb.ca)
Abraham Punnen(apunnen***at***sfu.ca)

Abstract: We consider a generalization of the well known greedy algorithm, called $m$-step greedy algorithm, where $m$ elements are examined in each iteration. When $m=1$ or $2$, the algorithm reduces to the standard greedy algorithm. For $m=3$ we provide a complete characterization of the independence system, called trioid, where the $m$-step greedy algorithm guarantees an optimal solution for all weight functions. We also characterize the trioid polytope and propose a generalization of submodular functions.

Keywords: matroid, trioid, submodular functions

Category 1: Combinatorial Optimization

Category 2: Combinatorial Optimization (Graphs and Matroids )

Category 3: Combinatorial Optimization (Polyhedra )

Citation: Manuscript, Department of Mathematics, Simnon Fraser University Surrey, 2009

Download: [PDF]

Entry Submitted: 08/10/2009
Entry Accepted: 08/11/2009
Entry Last Modified: 08/10/2009

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