Many future applications of computer networks such as distance education, remote collaboration, and teleconferencing will rely on the ability of the network to provide multicast services. We propose and evaluate ARIES, a heuristic for updating multicast trees dynamically in large point-to-point networks. The algorithm is based on monitoring the accumulated damage to the multicast tree within local regions or the tree as nodes are added and deleted and triggering a rearrangement when the number of changes within a connected subtree crosses a set threshold. We derive an analytical upper bound on the competitiveness of the algorithm. We also present simulation results to compare the average-case performance of the algorithm with two other known algorithms for the dynamic multicast problem, GREEDY, and edge-bounded algorithm (EBA). Our results show that ARIES provides the best balance among competitiveness, computational effort, and changes in the multicast tree after each update.

In this paper, we propose and evaluate ARIES, a heuristic for updating multicast trees dynamically in large point-to-point networks. The algorithm is based on monitoring the accumulated damage to the multicast tree within local regions of the tree as nodes are added and deleted, and triggering a rearrangement when the number of changes within a connected subtree crosses a set threshold. We derive an analytical upper-bound on the competitiveness of the algorithm. We also present simulation results to compare the average-case performance of the algorithm with two other known algorithms for the dynamic multicast problem, GREEDY and EBA (edge-bounded algorithm). Our results show that ARIES provides the best balance among competitiveness, computational effort, and changes in the multicast tree after each update.

Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area asynchronous transfer mode (ATM) network, can be modeled as the NP-complete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in point-to-point data networks. These algorithms are based on the centralized Steiner heuristics, the shortest path heuristic (SPH) and the Kruskal-based shortest path heuristic (K-SPH), and have the advantage that only the multicast members and nodes in the neighborhood of the multicast tree need to participate in the execution of the algorithm. We compare our algorithms by simulation against a baseline algorithm, the pruned minimum spanning-tree heuristic that is the basis of many previously published algorithms for finding multicast trees. Our results show that the competitiveness (the ratio of the sum of the heuristic tree's edge weights to that of the best solution found) of both of our algorithms was, on the average, 25% better in comparison to that of the pruned spanning-tree approach. In addition, the competitiveness of our algorithms was, in almost all cases, within 10% of the best solution found by any of the Steiner heuristics considered, including both centralized and distributed algorithms. Limiting the execution of the algorithm to a subset of the nodes in the network results in an increase in convergence time over the pruned spanning-tree approach, but this overhead can be reduced by careful implementation.

Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area ATM network, is often modeled as the NP-complete Steiner problem in networks. In this paper, we study algorithms for finding efficient multicast trees in the presence of constraints on the copying ability of the individual switch nodes in the network. We refer to this problem as the degree-constrained multicast tree problem and model it as the degree-constrained Steiner problem in networks. Steiner heuristics for the degree-constrained case are proposed and their simulation results for sparse, point-to-point networks are presented. The results are compared with respect to their quality of solution, cost (running time), and the number of test cases for which no solution could be found. The results of our research indicate that efficient multicast frees can be found in large, sparse networks with small multicast groups even with limited multicast capability in the individual switches. Some of the Steiner heuristics tested yielded degree-constrained multicast trees within 5% of the best heuristic solution found in most of the cases. Even when the fanout of each switch node was restricted to 2, the heuristics we used were able to generate efficient multicast trees in almost all our test networks. Surprisingly few test networks were unsolvable. In those cases where no solution was found by a heuristic, backtracking solved many of the remaining cases. Among the heuristics we used, degree-constrained versions of simple path-distance heuristics such as SPH and SPH-R provided the best tradeoffs between quality of solution and cost.