NETWORK REINFORCEMENT

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 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. 1