## Multicast Routing with End-to-End Delay and Delay Variation Constraints (1995)

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Venue: | IEEE Journal on Selected Areas in Communications |

Citations: | 71 - 2 self |

### BibTeX

@ARTICLE{Rouskas95multicastrouting,

author = {George N. Rouskas and Ilia Baldine},

title = {Multicast Routing with End-to-End Delay and Delay Variation Constraints},

journal = {IEEE Journal on Selected Areas in Communications},

year = {1995},

volume = {15},

pages = {346--356}

}

### OpenURL

### Abstract

We study the problem of constructing multicast trees to meet the quality of service requirements of real-time, interactive applications operating in high-speed packet-switched environments. In particular, we assume that multicast communication depends on (a) bounded delay along the paths from the source to each destination, and (b) bounded variation among the delays along these paths. We first establish that the problem of determining such a constrained tree is NP-complete. We then derive heuristics that demonstrate good average case behavior in terms of the maximum inter-destination delay variation of the final tree. In addition, our heuristics achieve their best performance under conditions typical of multicast scenarios in high-speed networks. We also show that it is possible to dynamically reorganize the initial tree in response to changes in the destination set, in a way that is minimally disruptive to the multicast session. Department of Computer Science North Carolina State Uni...

### Citations

1794 |
Data Networks
- Bertsekas, Gallager
- 1987
(Show Context)
Citation Context ...d locally at node s, making it possible to determine the multicast tree at the source itself. This information may be collected and updated using one of several existing topology-broadcast algorithms =-=[12]-=-. The sequence of actions taken by node s during the course of constructing a multicast tree is illustrated in the flowchart of Figure 1, where we have assumed that the values of the delay and delay v... |

1444 | A note on two problems in connexion with graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ... ffi, respectively, provided by the application are negotiable 1 . As a first step, the tree of shortest paths from s to all nodes in M is constructed; this can be achieved using Dijkstra's algorithm =-=[13]-=-, which, for dense graphs with n nodes, takes time O(n 2 ). Let T 0 be this tree of shortest paths. If T 0 does not satisfy the path delay constraint (1) no tree may satisfy it, implying that the dela... |

826 | A note on two problems in connection with graphs”. Numerische Mathematik, 1:260–271 - Dijkstra - 1959 |

642 |
Routing of multipoint connections
- Waxman
- 1988
(Show Context)
Citation Context ... multicast tree. The minimum cost tree is known as the Steiner tree [2], and finding such a tree is a well-known NP-complete problem [3]. Heuristics to construct low cost trees have been developed in =-=[4, 5, 6, 7]-=-. While total tree cost as a measure of bandwidth efficiency is certainly an important parameter, it is not sufficient to characterize the quality of the tree as perceived by interactive multimedia an... |

532 |
Shortest connection networks and some generalizations
- Prim
- 1957
(Show Context)
Citation Context ... source to any node in the network. The resulting tree is pruned to exclude paths that do not terminate at a destination node, and will be referred to as shortest path tree (SPT). 4. Prim's algorithm =-=[15]-=- which constructs a tree of minimum weight spanning all nodes in the network; in our case, the weight of each link is the delay incurred along the link. This minimum spanning tree (MST) is also pruned... |

450 | Combinatorial Optimization: Networks and Matroids - Lawler - 1976 |

274 |
Combinational Optimization: Networks and
- Lawler
- 1976
(Show Context)
Citation Context ... "while" loop. Then, the innermost loop starting at line 9 will iterate t j times; inside this loop the complexity is determined by the l-shortest path algorithm at line 11, which takes time=-= O(lN 3 ) [14]-=- for a graph with N nodes. Graph G 0 has n \Gamma t j + 1 nodes throughout the innermost loop; the latter then takes time proportional to lt j (n \Gamma t j + 1) 3 . For a worst case analysis, we let ... |

247 |
A fast algorithm for steiner trees
- Kou, Markowsky, et al.
- 1981
(Show Context)
Citation Context ...tree. The minimum cost tree is known as the Steiner tree [2], and finding such a tree is a well-known NP-complete problem [3]. Heuristics to construct trees of low overall cost have been developed in =-=[4, 5, 6, 7]-=-. While total tree cost as a measure of bandwidth efficiency is certainly an important parameter, it is not sufficient to characterize the quality of the tree as perceived by the interactive multimedi... |

219 |
New Directions in Communications (or Which Way to the Information Ap
- Turner
- 1986
(Show Context)
Citation Context ...s, all members of the same multicast group. Mechanisms to support such a form of communication are becoming an increasingly important component of the design and implementation of distributed systems =-=[1]-=-. One of the core issues that needs to be addressed as part of providing such mechanisms is the issue of routing, which primarily refers to the determination of a set of paths to be used for carrying ... |

189 | Multicast routing for multimedia communication
- Kompella, Pasquale, et al.
- 1993
(Show Context)
Citation Context ...s in terms of the end-to-end delay along the individual paths from the source to each of the destination nodes. The problem of routing multicast traffic with real-time constraints has been studied in =-=[8, 9]-=- and heuristics to compute low-cost trees which guarantee an upper bound on the end-to-end delay have been developed. For a survey and extensive simulation study of a large number of existing multicas... |

140 |
Steiner minimal trees
- Gilbert, Pollak
- 1968
(Show Context)
Citation Context ...tree. The minimum cost tree is known as the Steiner tree [2], and finding such a tree is a well-known NP-complete problem [3]. Heuristics to construct trees of low overall cost have been developed in =-=[4, 5, 6, 7]-=-. While total tree cost as a measure of bandwidth efficiency is certainly an important parameter, it is not sufficient to characterize the quality of the tree as perceived by the interactive multimedi... |

98 |
The Complexity of Computing Steiner Minimal Trees
- Garey, Graham, et al.
- 1977
(Show Context)
Citation Context ...he tree, which is taken as the sum of the costs on the links of the multicast tree. The minimum cost tree is known as the Steiner tree [2], and finding such a tree is a well-known NP-complete problem =-=[3]-=-. Heuristics to construct low cost trees have been developed in [4, 5, 6, 7]. While total tree cost as a measure of bandwidth efficiency is certainly an important parameter, it is not sufficient to ch... |

88 |
Routing to multiple destinations in computer networks
- Kumar, Jaffe
- 1983
(Show Context)
Citation Context ... multicast tree. The minimum cost tree is known as the Steiner tree [2], and finding such a tree is a well-known NP-complete problem [3]. Heuristics to construct low cost trees have been developed in =-=[4, 5, 6, 7]-=-. While total tree cost as a measure of bandwidth efficiency is certainly an important parameter, it is not sufficient to characterize the quality of the tree as perceived by interactive multimedia an... |

43 |
Steiners problem in graphs and its implications
- Hakimi
- 1971
(Show Context)
Citation Context ...sidered optimization objective is to minimize the total cost of the tree, which is taken as the sum of the costs on the links of the multicast tree. The minimum cost tree is known as the Steiner tree =-=[2]-=-, and finding such a tree is a well-known NP-complete problem [3]. Heuristics to construct low cost trees have been developed in [4, 5, 6, 7]. While total tree cost as a measure of bandwidth efficienc... |

5 |
Garcia-Luna-Aceves. A source-based algorithm for near-optimum delay-constrained multicasting
- Zhu, Parsa, et al.
- 1995
(Show Context)
Citation Context ...s in terms of the end-to-end delay along the individual paths from the source to each of the destination nodes. The problem of routing multicast traffic with real-time constraints has been studied in =-=[8, 9]-=- and heuristics to compute low-cost trees which guarantee an upper bound on the end-to-end delay have been developed. For a survey and extensive simulation study of a large number of existing multicas... |

5 |
Comparison of multicast routing algorithms for high-speed networks
- Salama, Reeves, et al.
- 1994
(Show Context)
Citation Context ... For a survey and extensive simulation study of a large number of existing multicast algorithms, and an evaluation of their performance in high-speed real-time environments, the reader is referred to =-=[10, 11]-=-. In this work we consider an additional criterion that can be used to characterize the quality of the multicast tree for interactive, real-time applications. In particular, we assume that, in additio... |

4 | Evaluation of Multicast Routing Algorithms for Distributed Real-Time Applications of High-Speed Networks - Salama, Reeves - 1995 |

1 | A Proof that Problem DVBMT is NP-complete We now show that problem DVBMT is NP-complete even when the number of destination nodes is j M j= 2. The proof uses a transformation from PARTITION, a well known NP-complete problem - Computers, Freeman, et al. - 1979 |