- Network Reinforcement Francisco Barahona (barahonus.ibm.com) Abstract: We give an algorithm for the following problem: given a graph $G=(V,E)$ with edge-weights and a nonnegative integer $k$, find a minimum cost set of edges that contains $k$ disjoint spanning trees. This also solves the following {\it reinforcement problem}: given a network, a number $k$ and a set of candidate edges, each of them with an associated cost, find a minimum cost set of candidate edges to be added to the network so it contains $k$ disjoint spanning trees. The number $k$ is seen as a measure of the invulnerability of a network. We show that this can be solved with $|V|$ applications of the minimum cut algorithm of Goldberg \& Tarjan. Keywords: spanning trees Category 1: Combinatorial Optimization (Graphs and Matroids ) Citation: Download: [PDF]Entry Submitted: 09/25/2003Entry Accepted: 09/26/2003Entry Last Modified: 03/09/2006Modify/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.