## Multicast Tree Generation in Networks with Asymmetric Links (1996)

Venue: | IEEE/ACM Transactions on Networking |

Citations: | 72 - 0 self |

### BibTeX

@ARTICLE{Ramanathan96multicasttree,

author = {S. Ramanathan},

title = {Multicast Tree Generation in Networks with Asymmetric Links},

journal = {IEEE/ACM Transactions on Networking},

year = {1996},

volume = {4},

pages = {558--568}

}

### Years of Citing Articles

### OpenURL

### Abstract

We formulate the problem of multicast tree generation as one of computing a directed Steiner tree of minimal cost. In this context, we present a polynomial-time algorithm that provides for tradeoff selection, using a single parameter , between the tree-cost (Steiner cost) and the runtime efficiency. Further, the same algorithm may be used for delay optimization or tree-cost minimization simply by configuring the value of appropriately. We present theoretical and experimental analysis characterizing the problem and the performance of our algorithm. Theoretically, we (1) show that it is highly unlikely that there exists a polynomial-time algorithm with a performance guarantee of constant times optimum cost, (2) introduce metrics for measuring the asymmetry of graphs, and (3) show that the worst-case cost of the tree produced by our algorithm is at most twice the optimum cost times the asymmetry, for two of these asymmetry metrics. For graphs with bounded asymmetry, this gives constant ...

### Citations

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Computers and Intractability: A Guide to the Theory of NP-Completeness
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- 1979
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Citation Context ...vant to this paper stems from the fields of both communication networks and algorithmic graph theory. The minimization of tree cost has traditionally been formulated as the Steiner Minimal Tree (SMT) =-=[1, 2]-=- problem. The SMT problem has been well studied from a purely graph theoretical point of view and a good survey can be found in [2, 3]. In particular, it has been shown that optimizing SMT is NP-compl... |

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Introduction to Algorithms
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Citation Context ...introduction, there do not exist any good approximation algorithms for DSMT. However, several problems such as the traveling salesman problem, although NP-complete, have good approximation algorithms =-=[18]-=-. Closer to home, the 2 Hereafter, unless otherwise indicated, we mean polynomial-time approximation algorithm 3 undirected Steiner tree problem has several good approximation algorithms. In particula... |

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Reducibility among combinatorial problems
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121 |
An Analysis of Several Heuristics for the Traveling Salesman Problem
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- 1977
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Citation Context ... \Psi g , the graph asymmetry and in terms of \Psi m , the maximum edge asymmetry. We make use of the the following lemma on the permutation of a set of integers, originally due to Rosenkrantz et al. =-=[20] and also -=-given in [5]. Lemma 4.1 Suppose t 1 , t 2 ... t k is a permutation of 1, 2, ... , k. Then for every i, 2sisk, there exists a unique "critical pair" (t j \Gamma1 , t j ) such that min(t j \Ga... |

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56 |
The computation of nearly minimal Steiner trees in graphs
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Citation Context ... multicast group membership is addressed in [11]. Cost minimization subject to constraints on maximum delay is considered in [12, 14], and a degree-constrained heuristic for Steiner trees is given in =-=[13]-=-. This work differs from previous works in three significant respects. First, all of the works mentioned above and most existing literature on the SMT problem assume the underlying graph to be undirec... |

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Citation Context ...casting in communication networks yield several interesting variants of the Steiner Minimal Tree problem. The application of Steiner tree heuristics to delay and cost minimization has been studied in =-=[10]-=-. The dynamism of multicast group membership is addressed in [11]. Cost minimization subject to constraints on maximum delay is considered in [12, 14], and a degree-constrained heuristic for Steiner t... |

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Citation Context ...nts of the Steiner Minimal Tree problem. The application of Steiner tree heuristics to delay and cost minimization has been studied in [10]. The dynamism of multicast group membership is addressed in =-=[11]-=-. Cost minimization subject to constraints on maximum delay is considered in [12, 14], and a degree-constrained heuristic for Steiner trees is given in [13]. This work differs from previous works in t... |

1 |
Ramanathan (M '92) received his B.Tech degree from the Indian Institute of Technology, Madras, and his Ph.D degree from the University of Delaware. He is a research scientist with the Advanced Networking Department at BBN Corporation, where he is currentl
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Citation Context ... to a vertex y is an alternating sequence of vertices and edges x, (x; u 1 ), u 1 , (u 1 ; u 2 ), .... , (u m ; y), y and is denoted by (x ; y). All graph-theoretic terminology not given here is from =-=[21]-=-. 2.2 Multicasting as a Directed Steiner Tree The problem considered in this paper is the generation of a source-rooted multicast tree. A source-rooted multicast tree is the directed Steiner tree (DST... |