Simple Greedy Algorithms for Fundamental Multidimensional Graph Problems

We revisit fundamental problems in undirected and directed graphs, such as the problems of computing spanning trees, shortest paths, steiner trees, and spanning arborescences of minimum cost. We assume that there are d different cost functions associated with the edges of the input graph and seek for solutions to the resulting multidimensional graph problems so that the p-norm of the different costs of the solution is minimized. We present combinatorial algorithms that achieve very good approximations for this objective. The main advantage of our algorithms is their simplicity: they are as simple as classical combinatorial graph algorithms of Dijkstra and Kruskal, or the greedy algorithm for matroids