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123
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 484 (21 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 general approximation technique for constrained forest problems
 in Proceedings of the 3rd Annual ACMSIAM Symposium on Discrete Algorithms
, 1992
"... Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimizatio ..."
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Cited by 355 (21 self)
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Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
Impact of network density on Data Aggregation in wireless sensor networks
, 2001
"... Innetwork data aggregation is essential for wireless sensor networks where resources (e.g., bandwidth, energy) are limited. In a previously proposed data dissemination scheme, data is opportunistically aggregated at the intermediate nodes on a lowlatency tree which may not necessarily be energy ef ..."
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Cited by 256 (4 self)
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Innetwork data aggregation is essential for wireless sensor networks where resources (e.g., bandwidth, energy) are limited. In a previously proposed data dissemination scheme, data is opportunistically aggregated at the intermediate nodes on a lowlatency tree which may not necessarily be energy efficient. A more energyefficient tree is a greedy tree which can be incrementally constructed by connecting each source to the closest point of the existing tree. In this paper, we propose a greedy approach for constructing a greedy aggregation tree to improve path sharing. We evaluated the performance of this greedy approach by comparing it to the prior opportunistic approach. Our preliminary result suggests that although the greedy aggregation and the opportunistic aggregation are roughly equivalent at lowdensity networks, the greedy aggregation can achieve signficant energy savings at higher densities. In one experiment we found that the greedy aggregation can achieve up to 45 % energy savings over the opportunistic aggregation without an adverse impact on latency or robustness.
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 219 (32 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.
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 134 (9 self)
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The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich and Widmayer and finds applications in VLSI design. The group Steiner tree problem generalizes the set covering problem, and is therefore at least as had. We give a randomized O(log 3 n log k)approximation algorithm for the group Steiner tree problem on an nnode graph, where k is the number of groups. The best previous ink)v/ (Bateman, Helvig, performance guarantee was (1 +  Robins and Zelikovsky).
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 123 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
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 122 (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...
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.
Greedy Randomized Adaptive Search Procedures For The Steiner Problem In Graphs
 QUADRATIC ASSIGNMENT AND RELATED PROBLEMS, VOLUME 16 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1999
"... We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions ..."
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Cited by 105 (29 self)
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We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions on a variety of test problems are reported. On the majority of instances from the ORLibrary, a set of standard test problems, the GRASP produced optimal solutions. On those that optimal solutions were not found, the GRASP found good quality approximate solutions.
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 104 (8 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.