Trees and electrical networks

Abstract

Given a connected graph G = (V,E) and a weight function w : E → ℚ, the minimum spanning tree problem asks for a spanning tree T = (V, F), F ⊂ E, for which Σ^e∊F w(e) is minimal. A greedy algorithm (GA) is as follows: in the initial step we choose a cheapest edge, and in each subsequent step we choose one among the cheapest remaining edges with the restriction that the subgraph of G formed by the selected edges is acyclic.