The Steiner path aggregation problem

Abstract

In the Steiner Path Aggregation Problem, our goal is to aggregate paths in a directed network into a single arborescence without significantly disrupting the paths. In particular, we are given a directed multigraph with colored arcs, a root, and k terminals, each of which has a monochromatic path to the root. Our goal is to find an arborescence in which every terminal has a path to the root, and its path does not switch colors too many times. We give an efficient algorithm that finds such a solution with at most $2{\log }_{\frac{4}{3}}k$ color switches. Up to constant factors this is the best possible universal bound, as there are graphs requiring at least ${\log }_{2}k$ color switches.