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80
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 162 (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...
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 144 (29 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
Achieving MinimumCost Multicast: A Decentralized Approach Based on Network Coding
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumco ..."
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Cited by 105 (15 self)
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We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumcost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixedrate multicast in networks with directed pointtopoint links, and consider the problem of minimumenergy multicast in wireless networks as well as the case of a concave utility function at the sender.
Evaluation of Multicast Routing Algorithms for RealTime Communication on HighSpeed Networks
 IEEE Journal on Selected Areas in Communications
, 1997
"... Abstract—Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric li ..."
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Cited by 91 (4 self)
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Abstract—Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. Each algorithm is judged based on the quality of the MC trees it generates and its efficiency in managing the network resources. Simulation results over random networks show that unconstrained algorithms are not capable of fulfilling the QoS requirements of realtime applications in widearea networks. Simulations also reveal that one of the unconstrained algorithms, reverse path multicasting (RPM), is quite inefficient when applied to asymmetric networks. We study how combining routing with resource reservation and admission control improves RPM’s efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, Kompella, Pasquale, and Polyzos (KPP), constrained adaptive ordering (CAO), and bounded shortest multicast algorithm (BSMA), and one constrained shortest path tree (CSPT) heuristic, the constrained Dijkstra heuristic (CDKS) are also studied. Simulations show that the semiconstrained and constrained heuristics are capable of successfully constructing MC trees which satisfy the QoS requirements of realtime traffic. However, the cost performance of the heuristics varies. BSMA’s MC trees are lower in cost than all other constrained heuristics. Finally, we compare the execution times of all algorithms, unconstrained, semiconstrained, and constrained. Index Terms—Admission control, multicast routing, quality of service, reverse path multicasting. I.
Redundant trees for preplanned recovery in arbitrary vertex—Redundant or edge redundant graphs
 IEEE/ACM Trans. Netw
, 1999
"... Abstract—We present a new algorithm which creates redundant trees on arbitrary noderedundant or linkredundant networks. These trees are such that any node is connected to the common root of the trees by at least one of the trees in case of node or link failure. Our scheme provides rapid preplanned ..."
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Cited by 68 (4 self)
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Abstract—We present a new algorithm which creates redundant trees on arbitrary noderedundant or linkredundant networks. These trees are such that any node is connected to the common root of the trees by at least one of the trees in case of node or link failure. Our scheme provides rapid preplanned recovery of communications with great flexibility in the topology design. Unlike previous algorithms, our algorithm can establish two redundant trees in the case of a node failing in the network. In the case of failure of a communications link, our algorithm provides a superset of the previously known trees. Index Terms—Graph theory, multicasting, network recovery, network robustness, routing, trees. I.
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 37 (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.
A Unicastbased Approach for Streaming Multicast
, 2001
"... Network layer multicast is know as the most efficient way to support multicast sessions. However, for security, QoS and other considerations, most of the realtime application protocols can be better served by upper layer (transport or application) multicast. In this paper we propose a scheme called ..."
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Cited by 31 (0 self)
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Network layer multicast is know as the most efficient way to support multicast sessions. However, for security, QoS and other considerations, most of the realtime application protocols can be better served by upper layer (transport or application) multicast. In this paper we propose a scheme called MRTP for multicast RTP sessions. The idea behind this scheme is to set up the multicast RTP session over a set of unicast RTP sessions, established between the various participants (source and destinations) of the multicast session. We then address the issue of finding a set of paths with maximum bottleneck for an MRTP session. We show that this problem is NPComplete, and propose several heuristics to solve it.
Subpath Protection for Scalability and Fast Recovery in Optical . . .
, 2004
"... This paper investigates survivable lightpath provisioning and fast protection switching for generic meshbased optical networks employing wavelengthdivision multiplexing (WDM). We propose subpath protection, which is a generalization of sharedpath protection. The main ideas of subpath protection ..."
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Cited by 24 (5 self)
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This paper investigates survivable lightpath provisioning and fast protection switching for generic meshbased optical networks employing wavelengthdivision multiplexing (WDM). We propose subpath protection, which is a generalization of sharedpath protection. The main ideas of subpath protection are: 1) to partition a large optical network into smaller domains and 2) to apply sharedpath protection to the optical network such that an intradomain lightpath does not use resources of other domains and the primary/backup paths of an interdomain lightpath exit a domain (and enter another domain) through a common domainborder node. We mathematically formulate the routing and wavelengthassignment (RWA) problem under subpath protection for a given set of lightpath requests, prove that the problem is NPcomplete, and develop a heuristic to find efficient solutions. Comparisons between subpath protection and sharedpath protection on a nationwide network with dozens of wavelengths per fiber show that, for a modest sacrifice in resource utilization, subpath protection achieves improved survivability, much higher scalability, and significantly reduced faultrecovery time.
A Graph Theoretic Approach to Bounding Delay in ProxyAssisted, EndSystem Multicast
 in ProxyAssisted, EndSystem Multicast. In Proc. of IWQoS
, 2002
"... Endsystem multicast provides a lowcost solution to scalably broadcast information to groups of users. However, lastmile bandwidth limitations constrain tree fanouts leading to high endtoend delivery delays. These delays can be reduced if the network provides forwarding proxies with high fanout c ..."
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Cited by 24 (1 self)
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Endsystem multicast provides a lowcost solution to scalably broadcast information to groups of users. However, lastmile bandwidth limitations constrain tree fanouts leading to high endtoend delivery delays. These delays can be reduced if the network provides forwarding proxies with high fanout capabilities at an additional cost. We use simple graph theoretic network models to explore the problem of building hybrid proxy/endsystem application layer multicast trees that meet fixed endtoend delay bounds. Our goal is to meet a fixed delay bound while minimizing costs associated with the utilization of proxies. We provide an algorithm and formally prove its optimality in a fullyconnected overlay network with uniformlength edges. We then adapt this algorithm into a heuristic and evaluate the heuristic for simulated transitstub networks with variabledelay edges. We compare our heuristic in a proxyfree environment to previously developed heuristics and show that our heuristic typically yields further reductions in the maximum session endtoend delay.
Dynamic routing of bandwidth guaranteed paths with local restoration
 Journal of Selected Area of Communication (JSAC
"... The emerging MultiProtocol Label Switching (MPLS) networks enable network service providers to route bandwidth guaranteed paths between customer sites [3, 2, 8, 5]. This basic Label Switched Path (LSP) routing is often enhanced using restoration routing which sets up alternate LSPs to guarantee uni ..."
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Cited by 20 (2 self)
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The emerging MultiProtocol Label Switching (MPLS) networks enable network service providers to route bandwidth guaranteed paths between customer sites [3, 2, 8, 5]. This basic Label Switched Path (LSP) routing is often enhanced using restoration routing which sets up alternate LSPs to guarantee uninterrupted connectivity in case network links or nodes along primary path fail. In this paper, we address the problem of distributed routing of restoration paths, which can be defined as follows: given a request for a bandwidth guaranteed LSP between two nodes, find a primary LSP and a set of backup LSPs that protect the links along the primary LSP. A routing algorithm that computes these paths must optimize the restoration latency and the amount of bandwidth used.