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58
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...
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 110 (28 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 86 (14 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
"... 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. ..."
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Cited by 78 (4 self)
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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, KPP, CAO, and BSMA, and one constrained shortest path tree (CSPT) 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.
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 29 (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.
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.
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 20 (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 20 (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.
A Scalable Approach for DiffServ Multicasting
, 2001
"... The phenomenal growths of group communications and QoSaware applications over the Internet have respectively accelerated the development of two key technologies, namely, multicasting and Differentiated Services (DiffServ). Although both are complementary technologies, the integration of the two tec ..."
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Cited by 18 (7 self)
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The phenomenal growths of group communications and QoSaware applications over the Internet have respectively accelerated the development of two key technologies, namely, multicasting and Differentiated Services (DiffServ). Although both are complementary technologies, the integration of the two technologies is a nontrivial task due to architectural conflicts between multicasting and DiffServ. In this paper, we propose an approach for providing multicast support across a DiffServ domain that is scalable in terms of group size, network size, and number of groups. We analyze our approach in a detailed manner for feasibility, adaptiveness, and deployment considerations.
Online Multicast Routing with Bandwidth Guarantees: A New Approach using Multicast Network Flow
, 2000
"... This paper presents a new algorithm for online routing of bandwidthguaranteed multicasts where routing requests arrive onebyone without there being any a priori knowledge of future requests. A multicast routing request consists of a source s, a set of receivers R, and a bandwidth requirement b. ..."
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Cited by 17 (1 self)
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This paper presents a new algorithm for online routing of bandwidthguaranteed multicasts where routing requests arrive onebyone without there being any a priori knowledge of future requests. A multicast routing request consists of a source s, a set of receivers R, and a bandwidth requirement b. This multicast routing problem arises in many contexts. Two applications of interest are routing of pointtomultipoint labelswitched paths in MultiProtocol Label Switched (MPLS) networks, and the provision of bandwidth guaranteed Virtual Private Network (VPN) services under the "hose" service model [18]. Offline multicast routing algorithms cannot be used since they require a priori knowledge of all multicast requests that are to be routed. Instead, online algorithms that handle requests arriving onebyone and that satisfy as many potential future demands as possible are needed. The newly developed algorithm is an online algorithm and is based on the idea that a newly routed multicast must follow a route that does not "interfere too much" with network paths that may be critical to satisfy future demands. We develop a multicast tree selection heuristic that is based on the idea of deferred loading of certain "critical" links. These critical links are identified by the algorithm as links that, if heavily loaded, would make it impossible to satisfy future demands between certain ingressegress pairs. The presented algorithm uses linkstate information and some auxilliary capacity information for multicast tree selection and is amenable to distributed implementation. Unlike previous algorithms, the proposed algorithm exploits any available knowledge of the network ingressegress points of potential future demands even though the demands themselves are unknown and performs very well.