An algorithm for multicast tree generation in networks with asymmetric links

We formulate the problem of multicast tree generation in asymmetric networks as one of computing a directed Steiner tree of minimal cost. We present a new polynomial-time algorithm that provides for trade-off selection, using a single parameter κ, between the tree-cost (Steiner cost) and the runtime efficiency. Using theoretical analysis, we (1) show that it is highly unlikely that there exists a polynomial-time algorithm with a performance guarantee of constant times optimum cost, (2) introduce metrics for measuring the asymmetry of graphs, and (3) show that the worst-case cost of the tree produced by our algorithm is bounded in proportion to the graph asymmetry for two of the metrics. For a class of graphs whose asymmetry is upper bounded by a constant, this gives constant times optimum performance guarantee and is significant in light of (1). We also show that three well-known algorithms for (undirected) Steiner trees are but particular cases of our algorithm. Our experimental study shows that operating at a low κ gives nearly best possible average tree cost while maintaining acceptable runtime efficiency