Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or membership report information are occasionally sent over many links that do not lead to receivers or senders, respectively. Wehave developed a multicast routing architecture that efficiently establishes distribution trees across wide area internets, where many groups will be sparsely represented. Efficiency is measured in terms of the state, control message processing, and data packet processing, required across the entire network in order to deliver data packets to the members of the group. Our Protocol Independent Multicast (PIM) architecture: (a) maintains the traditional IP multicast service model of receiver-initiated membership; (b) can be configured to adapt to different multicast group and network characteristics; (c) is not dependent on a specific unicast routing protocol; and (d) uses soft-state mechanisms to adapt to underlying network conditions and group dynamics. The robustness, flexibility, and scaling properties of this architecture make it well suited to large heterogeneous inter-networks.

Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "well-known" topologies such as the ARPAnet, and randomly generated topologies. While many researchers rely upon graphs for analytic and simulation studies, there has been little analysis of the implications of using a particular model, or how the graph generation method may a ect the results of such studies. Further, the selection of one generation method over another is often arbitrary, since the differences and similarities between methods are not well understood. This paper considers the problem of generating and selecting graph models that reflect the properties of real internetworks. We review generation methods in common use, and also propose several new methods. We consider a set of metrics that characterize the graphs produced by a method, and we quantify similarities and differences amongst several generation methods with respect to these metrics. We also consider the effect of the graph model in the context of a speciffic problem, namely multicast routing.

We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with link-costs and, for each pair fi; jg of nodes, an edge-connectivity requirement r ij . The goal is to find a minimum-cost network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2dlog 2 (r + 1)e of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial min-max approximate equality relating minimum-cost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.

We present heuristics for multicast tree construction for communication that depends on: i) bounded end-to-end delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such a constrained multicast tree is NP-complete. We show that the heuristics demonstrate good average case behavior in terms of cost, as determined through simulations on a large number of graphs.

The up-coming Gbps high-speed networks are expected to support a wide range of communication-intensive, real-time multimedia applications. The requirement for timely delivery of digitized audio-visual information raises new challenges for the next generation integrated-service broadband networks. One of the key issues is the Quality-of-Service (QoS) routing. It selects network routes with sufficient resources for the requested QoS parameters. The goal of routing solutions is two-fold: (1) satisfying the QoS requirements for every admitted connection and (2) achieving the global efficiency in resource utilization. Many unicast/multicast QoS routing algorithms were published recently, and they work with a variety of QoS requirements and resource constraints. Overall, they can be partitioned into three broad classes: (1) source routing, (2) distributed routing and (3) hierarchical routing algorithms. In this paper we give an overview of the QoS routing problem as well as the existing solutions. We present the strengths and the weaknesses of different routing strategies and outline the challenges. We also discuss the basic algorithms in each class, classify and compare them, and point out possible future directions in the QoS routing area.

Much of the work on routing algorithms, particularly for multicast, which has been done in the past has used fairly simple models to generate the topological graph which represents the nodes in the network. Some such random graphs bear little resemblance to data communication networks which are actually deployed. This paper proposes a more realistic model for such random networks and describes various scenarios which can be more accurately represented. The approach described here can be developed to provide more refined models in the future, and the source code of an implementation is freely available. 1.0 INTRODUCTION One of the major areas of interest in recent routing research has been how to route multicast packets in a connection-oriented network such as an IP network, and similarly, how to set up multicast connections in a connection-oriented network, such as an ATM network. Many algorithms have been described in the literature. Some produce an optimal solution [Karp72] but many...

Multicast trees can be shared across sources (shared trees) or may be source-specific (shortest path trees). Inspired by recent interests in using shared trees for interdomain multicasting, we investigate the trade-offs among shared tree types and source specific shortest path trees, by comparing performance over both individual multicast group and the whole network. The performance is evaluated in terms of path length, link cost, and traffic concentration. We present simulation results over a real network as well as random networks under different circumstances. One practically significant conclusion is that member- or sendercentered trees have good delay and cost properties on average, but they exhibit heavier traffic concentration which makes them inappropriate as the universal form of trees for all types of applications. Keywords: Multicast, Routing, Scalability, Center Placement Strategy 1 Introduction Multimedia communication is often multi-point and has contributed to the dem...

When the problem of routing multicast connections in networks has been previously considered, the aim has been to minimise overall costs, possibly subject to a delay constraint. The emphasis has been on examining the problem with a source transmitting to a fixed set of destinations (the multicast group) which are known when communication is established. There are clearly some applications for which the set of destinations will be dynamic, with destinations joining and leaving the multicast group during the communication. Under these conditions the computation of an "optimal " spanning tree for each new multicast group may not be the best way to proceed. An alternative is to make modest alterations to an existing spanning tree to derive a new one. An extreme variation of this is to use minimal cost source to destination routing for each destination, effectively ignoring the existing multicast tree. This naive approach leads to a simple implementation but clearly produces non-optimal spa...

We give the first non-trivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work were the trivial O(k)-approximations. For the directed Steiner tree problem, we design a family of algorithms that achieves an approximation ratio of i(i \Gamma 1)k 1=i in time O(n i k 2i ) for any fixed i ? 1, where k is the number of terminals. Thus, an O(k ffl ) approximation ratio can be achieved in polynomial time for any fixed ffl ? 0. Setting i = log k, we obtain an O(log 2 k) approximation ratio in quasi-polynomial time. For the directed generalized Steiner network problem, we give an algorithm that achieves an approximation ratio of O(k 2=3 log 1=3 k), where k is the number of pairs of vertices that are to be connected. Related problems including the group Steiner...

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