Cs 598csc: Combinatorial Optimization 1 Spanning Trees

Abstract

Let G = (V,E) be an undirected graph and let c : E → R be an edge-cost function. Efficient polynomial time algorithms for computing a minimum cost spanning tree (MST) are standard. Spanning trees in G are bases in the associated graphic matroid and Kruskal’s algorithm for MST is the essentially the greedy algorithm for computing a minimum cost base in a matroid. From polyhedral results on matroids we obtain corresponding results for spanning trees. The spanning tree polytope of G = (V,E) is the polytope formed by the convex hull of the characteristic vectors of spanning trees of G, and is determined by the following inequalities. We have a variable x(e) for each e ∈ E and for a set U ⊆ V , E[U ] is the set of edges with both end points in U . x(E) = n− 1

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Cite this paper

@inproceedings{Gao2010Cs5C, title={Cs 598csc: Combinatorial Optimization 1 Spanning Trees}, author={Jing Gao}, year={2010} }