On the Broadcast Routing Problem

02/25/2018

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by   Brahim Chaourar, et al.

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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∈^E_+, k(G, w) is the w-maximum packing of r-arborescences for all r∈ V and all r-acyclic 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.