On the Broadcast Routing Problem

Given an undirected graph G = (V,E), and a vertex r ∈ V , an r-acyclic orientation of G is an orientation OE of the edges of G such that the digraph OG = (V,OE) is acyclic and r is the unique vertex with indegree equal to 0. For w ∈ RE+, k(G,w) is the w-maximum packing of r-arborescences for all r ∈ V and all racyclic orientations OE of G. In this case, the Broadcast Routing (in Computers Networks) Problem (BRP) is to compute k(G,w), by finding an optimal r and an optimal r-acyclic orientation. BRP is a mathematical formulation of multipath broadcast routing in computer networks. In this paper, we provide a polynomial time algorithm to solve BRP in outerplanar graphs. Outerplanar graphs are encountered in many applications such computational geometry, robotics, etc. 2010 Mathematics Subject Classification: Primary 90C27, Secondary 94C99.