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An Architecture for WideArea Multicast Routing
"... 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 ..."
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Cited by 529 (22 self)
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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 receiverinitiated 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 softstate 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 internetworks.
A quantitative comparison of graphbased models for internet topology
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... 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, "wellknown" topologies such as the ARPAnet, and ..."
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Cited by 266 (3 self)
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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, "wellknown" 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.
When trees collide: An approximation algorithm for the generalized Steiner problem on networks
, 1994
"... We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the a ..."
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Cited by 256 (39 self)
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We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost 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 minmax approximate equality relating minimumcost 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.
An Overview of QualityofService Routing for the Next Generation HighSpeed Networks: Problems and Solutions
"... The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. On ..."
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Cited by 223 (22 self)
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The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. One of the key issues is the QualityofService (QoS) routing. It selects network routes with sufficient resources for the requested QoS parameters. The goal of routing solutions is twofold: (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.
Multicast Routing for Multimedia Communication
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1993
"... We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend 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 ..."
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Cited by 216 (9 self)
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We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend 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 NPcomplete. We show that the heuristics demonstrate good average case behavior in terms of cost, as determined through simulations on a large number of graphs.
A Better Model for Generating Test Networks
, 1996
"... 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 actu ..."
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Cited by 177 (1 self)
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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 connectionoriented network such as an IP network, and similarly, how to set up multicast connections in a connectionoriented network, such as an ATM network. Many algorithms have been described in the literature. Some produce an optimal solution [Karp72] but many...
Approximation Algorithms for Directed Steiner Problems
 Journal of Algorithms
, 1998
"... We give the first nontrivial 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 we ..."
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Cited by 177 (8 self)
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We give the first nontrivial 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 quasipolynomial 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...
A nearly bestpossible approximation algorithm for nodeweighted Steiner trees
, 1993
"... We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems. ..."
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Cited by 138 (10 self)
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We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems.
Applications of Approximation Algorithms to Cooperative Games
 STOC'01
, 2001
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The Tradeoffs of Multicast Trees and Algorithms
, 1994
"... Multicast trees can be shared across sources (shared trees) or may be sourcespecific (shortest path trees). Inspired by recent interests in using shared trees for interdomain multicasting, we investigate the tradeoffs among shared tree types and source specific shortest path trees, by comparing pe ..."
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Cited by 134 (6 self)
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Multicast trees can be shared across sources (shared trees) or may be sourcespecific (shortest path trees). Inspired by recent interests in using shared trees for interdomain multicasting, we investigate the tradeoffs 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 multipoint and has contributed to the dem...