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54
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 143 (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 Distributed Algorithm for DelayConstrained Unicast Routing
 IEEE INFOCOM'97
, 1997
"... In this paper, we study the NPhard delayconstrained leastcost path problem, and propose a simple, distributed heuristic solution: the delayconstrained unicast routing (DCUR) algorithm. DCUR requires limited network state information to be kept at each node: a cost vector and a delay vector. We p ..."
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Cited by 88 (1 self)
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In this paper, we study the NPhard delayconstrained leastcost path problem, and propose a simple, distributed heuristic solution: the delayconstrained unicast routing (DCUR) algorithm. DCUR requires limited network state information to be kept at each node: a cost vector and a delay vector. We prove DCUR's correctness by showing that it is always capable of constructing a loopfree delayconstrained path within finite time, if such a path exists. The worst case message complexity of DCUR is O(V³) messages, where V is the number of nodes. However, simulation results show that,on the average, DCUR requires much fewer messages. Therefore, DCUR scales well to large networks. We also use simulation to compare DCUR to the optimal algorithm, and to the leastdelay path algorithm. Our results show that DCUR's path costs are within 10% from those of the optimal solution.
Pricing Multicast Communication: A CostBased Approach
 Telecommunication Systems
, 2001
"... Multicast and unicast traffic share and compete for network resources. A costbased approach to multicast pricing, based on accurate characterization of multicast scalability, will facilitate the efficient and equitable resource allocation between traffic types. Through the quantification of link us ..."
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Cited by 72 (0 self)
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Multicast and unicast traffic share and compete for network resources. A costbased approach to multicast pricing, based on accurate characterization of multicast scalability, will facilitate the efficient and equitable resource allocation between traffic types. Through the quantification of link usage, this paper establishes a multicast scaling relationship: the cost of a multicast distribution tree varies at the 0.8 power of the multicast group size. This result is validated with both real and generated networks, and is robust across topological styles and network sizes. Since multicast cost can be accurately predicted given the membership size, there is strong motivation to price multicast according to membership size. Furthermore, a price ceiling should be set to account for the effect of tree saturation. This tariff structure is superior to either a purely membershipbased or a flatrate pricing scheme, since it reflects the actual tree cost at all group membership levels. Keywords: multicast pricing, multicast scaling 1.
An Iterative Algorithm for DelayConstrained MinimumCost Multicasting
 IEEE/ACM Transactions on Networking
, 1998
"... The bounded shortest multicast algorithm (BSMA) is presented for constructing minimumcost multicast trees with delay constraints. BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing ..."
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Cited by 45 (1 self)
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The bounded shortest multicast algorithm (BSMA) is presented for constructing minimumcost multicast trees with delay constraints. BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing tree. Instead of the singlepass tree construction approach used in most previous heuristics, the new algorithm is based on a feasiblesearch optimization strategy that starts with the minimumdelay multicast tree and monotonically decreases the cost by iterative improvement of the delaybounded multicast tree. BSMA's expected time complexity is analyzed, and simulation results are provided showing that BSMA can achieve nearoptimal cost reduction with fast execution.
Alternate Path Routing for Multicast
, 2000
"... Alternate path routing has been wellexplored in telecommunication networks as a means of decreasing the call blocking rate and increasing network utility. However, aside from some work applying these concepts to unicast flows, alternate path routing has received little attention in the Internet com ..."
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Cited by 29 (0 self)
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Alternate path routing has been wellexplored in telecommunication networks as a means of decreasing the call blocking rate and increasing network utility. However, aside from some work applying these concepts to unicast flows, alternate path routing has received little attention in the Internet community. We describe and evaluate an architecture for alternate path routing for multicast flows. For path installation, we design a receiveroriented alternate path protocol and prove that it reconfigures multicast trees without introducing loops. For path computation, we propose a scalable local search heuristic that allows receivers to find alternate paths using only partial network information. We use a simulation study to demonstrate the ability of local search to find alternate paths approximately as well as a linkstate protocol, with much lower overhead. I.
Search Space Reduction in QoS Routing
 In Proceedings of the 19th International Conference on Distributed Computing Systems
, 2001
"... To provide realtime service or engineer constrainedbased paths, networks require the underlying routing algorithm to be able to find lowcost paths that satisfy given QualityofService (QoS) constraints. However, the problem of constrained... ..."
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Cited by 29 (3 self)
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To provide realtime service or engineer constrainedbased paths, networks require the underlying routing algorithm to be able to find lowcost paths that satisfy given QualityofService (QoS) constraints. However, the problem of constrained...
A Survey of Combinatorial Optimization Problems in Multicast Routing
, 2003
"... In multicasting routing, the main objective is to send data from one or more source to multiple destinations, while at the same time minimizing the usage of resources. Examples of resources which can be minimized include bandwidth, time and connection costs. In this paper we survey applications of c ..."
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Cited by 27 (1 self)
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In multicasting routing, the main objective is to send data from one or more source to multiple destinations, while at the same time minimizing the usage of resources. Examples of resources which can be minimized include bandwidth, time and connection costs. In this paper we survey applications of combinatorial optimization to multicast routing. We discuss the most important problems considered in this area, as well as their models. Algorithms for each of the main problems are also presented.
QDMR: An Efficient QoS Dependent Multicast Routing Algorithm
 Proceeding of 5 th IEEE realtime technology and application symposium (RTAS ’99
, 1998
"... Many distributed realtime applications, such as audio and videoconferencing and collaborative systems, require multicast support from the underlying network. Multicasting involves the delivery of messages over a tree rooted at the sender and whose paths lead to the various receivers. A major obje ..."
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Cited by 21 (0 self)
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Many distributed realtime applications, such as audio and videoconferencing and collaborative systems, require multicast support from the underlying network. Multicasting involves the delivery of messages over a tree rooted at the sender and whose paths lead to the various receivers. A major objective of the routing protocol is to build a tree with minimum cost. Finding such a tree is known to be computationally expensive, and many heuristics have been proposed to efficiently find nearoptimal trees. Moreover, some heuristics exist to efficiently find multicast trees that are of low cost and satisfy QualityofService (QoS) (e.g. delay) delivery constraints required by realtime applications. However, these heuristics are not fast enough for largescale networks. In this paper, we present a fast algorithm, called QDMR, for generating delayconstrained lowcost multicast routing trees. A salient feature of QDMR is that it dynamically adjusts its lowcost tree construction policy base...
QoSAware Multicast Routing for the Internet: The Design and Evaluation of QoSMIC
 IEEE/ACM Transactions on Networking
, 2000
"... One of the main problems of the current Internet infrastructure is its inability to provide services at consistent QoS levels. At the same time, many emerging Internet applications, such as teleeducation, and teleconferencing, require multicast protocols that will provide the necessary Quality of ..."
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Cited by 17 (1 self)
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One of the main problems of the current Internet infrastructure is its inability to provide services at consistent QoS levels. At the same time, many emerging Internet applications, such as teleeducation, and teleconferencing, require multicast protocols that will provide the necessary Quality of Service (QoS). In this paper, we propose QoSMIC, a multicast routing protocol for the Internet, that provides QoSsensitive paths in a scalable, resourceefficient and flexible way. QoSMIC differs from the previous protocols in that it identifies multiple paths and selects the one that can provide the required QoS. Two other key advantages of QoSMIC are its exibility and adaptivity. First, the distribution tree does not have to be rooted at a preselected core router. Second, we can tradeoff between efficiency metrics depending on our needs; for example we can tradeoff routing efficiency for a reduction in the control messages. Extensive simulations show that our protocol improves the resources utilization and the endtoend performance compared to the current protocols. Specifically, our protocol reduces the call blocking probability by a factor of six and reduces the endtoend delay by as much as 90% compared to the PIM protocol.
ReceiverInitiated Multicast with Multiple QoS Constraints
 Proceedings of IEEE INFOCOM
, 1999
"... In this report we present our work on a receiverinitiated approach called RIMQoS to support multicast with multiple QoS constraints and dynamic memberships. Assuming linkstate information is available, a receiver computes a path to join the multicast tree rooted at the source. It then sends join r ..."
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Cited by 14 (3 self)
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In this report we present our work on a receiverinitiated approach called RIMQoS to support multicast with multiple QoS constraints and dynamic memberships. Assuming linkstate information is available, a receiver computes a path to join the multicast tree rooted at the source. It then sends join request along the path to join the group. We first present the operation of our approach in an intradomain setting with delay constraint. Then we introduce an algebraic formulation for multiple QoS constraints to show how to determine if QoS requirements for a new receiver can be satisfied at an intermediate node along the join path and how to adjust the tree without breaking QoS requirements for existing members if they are not. It attempts to minimize the cost of the tree by letting a node to join the tree via a lowcost path and may later switch to a highercost but more QoS stringent path when necessary. Our scheme builds multicast tree incrementally and thus supports fully dynamic memberships. It also supports of heterogeneous receivers seamlessly. Moreover, it can support any number of arbitrary QoS metrics without assuming any dependencies among them, if they satisfy some normal mathematical property. If implemented as a distributed routing protocol, our approach doesn't require any node to have explicit knowledge of the multicast tree topology, thus it scales well for multicast of large group. Simulation studies have been carried out to study its behavior and compare its performance with other schemes.