## Many-to-Many Routing on Trees via Matchings (1996)

Citations: | 10 - 4 self |

### BibTeX

@MISC{Pantziou96many-to-manyrouting,

author = {Grammati E. Pantziou and Alan Roberts and Antonis Symvonis},

title = {Many-to-Many Routing on Trees via Matchings},

year = {1996}

}

### OpenURL

### Abstract

In this paper we present an extensive study of many-to-many routing on trees under the matching routing model. Our study includes on-line and off-line algorithms. We present an asymptotically optimal on-line algorithm which routes k packets to their destination within d(k \Gamma 1) + d \Delta dist routing steps, where d is the degree of tree T on which the routing takes place and dist is the maximum distance any packet has to travel. We also present an off-line algorithm that solves the same problem within 2(k \Gamma 1)+dist steps. The analysis of our algorithms is based on the establishment of a close relationship between the matching and the hot-potato routing models that allows us to apply tools which were previously used exclusively in the analysis of hot-potato routing.

### Citations

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Citation Context ... r (2,3) r (1,2) (2,4) r (2,5) (2,6) (1,3) r (2,7) r (2,8) r (2,9) r Level-0 node Level-2 nodes Level-1 nodes Level-0 edges Level-1 edges Fig. 1. A complete ternary tree. transposition sorting method =-=[6, 1]-=-. Algorithm Odd-Even Heap Construction(T ) /* W.l.o.g., we assume that all key-values associated with the packets are distinct */ 1. Assign label h(T ) \Gamma (i + 1) to each level-i edge, 0si ! h(T )... |

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Citation Context ...bstract. In this paper we consider the routing number of trees, denoted by rt(), with respect to the matching routing model. The only known result is that rt(T )s3n for an arbitrary tree T of n nodes =-=[2, 3]-=-. By providing off-line permutation routing algorithms we prove that: i) rt(T )sn + o(n) for a complete d-ary tree T of n nodes, ii) rt(T )s2n + o(n) for an arbitrary bounded degree tree T of n nodes,... |

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Citation Context ...is is the only known work on routing on trees under the matching model. Algorithms for routing permutations on trees under different routing models have been presented by Borodin, Rabani and Schieber =-=[4]-=- (hot-potato routing model) and Symvonis [9] (simplified routing model). In our attempt to obtain an upper bound on the routing number of complete d-ary trees, we run into a problem of independent int... |

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Citation Context ...ested in forming the heap in the smallest number of parallel routing steps when routing is performed according to the matching routing model. Heaps are also discussed in the context of the PRAM model =-=[5, 7, 10]-=-. Rao and W. Zhang [7] and W. Zhang and Korf [10] described how to construct a heap (implemented as a complete binary tree) of n elements within 2 log 2 n steps. 1.1 Our Results In this paper, we cons... |

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Citation Context ... r (2,3) r (1,2) (2,4) r (2,5) (2,6) (1,3) r (2,7) r (2,8) r (2,9) r Level-0 node Level-2 nodes Level-1 nodes Level-0 edges Level-1 edges Fig. 1. A complete ternary tree. transposition sorting method =-=[6, 1]-=-. Algorithm Odd-Even Heap Construction(T ) /* W.l.o.g., we assume that all key-values associated with the packets are distinct */ 1. Assign label h(T ) \Gamma (i + 1) to each level-i edge, 0si ! h(T )... |

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Citation Context ...ested in forming the heap in the smallest number of parallel routing steps when routing is performed according to the matching routing model. Heaps are also discussed in the context of the PRAM model =-=[5, 7, 10]-=-. Rao and W. Zhang [7] and W. Zhang and Korf [10] described how to construct a heap (implemented as a complete binary tree) of n elements within 2 log 2 n steps. 1.1 Our Results In this paper, we cons... |

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Citation Context ...ested in forming the heap in the smallest number of parallel routing steps when routing is performed according to the matching routing model. Heaps are also discussed in the context of the PRAM model =-=[5, 7, 10]-=-. Rao and W. Zhang [7] and W. Zhang and Korf [10] described how to construct a heap (implemented as a complete binary tree) of n elements within 2 log 2 n steps. 1.1 Our Results In this paper, we cons... |

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(Show Context)
Citation Context ...tion subtrees. The routing is then completed recursively. Given a subtree T 0 , Alon, Chung and Graham describe a greedy method to construct a partial tree rooted at its root within jT 0 j steps (see =-=[2, 3]-=- for details). By realizing that the heap-ordering algorithm described in this paper can be also used to achieve the same goal, we conclude that the routing of the first phase on subtree T 0 can be co... |

3 | Optimal algorithms for packet routing on trees
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(Show Context)
Citation Context ...s under the matching model. Algorithms for routing permutations on trees under different routing models have been presented by Borodin, Rabani and Schieber [4] (hot-potato routing model) and Symvonis =-=[9]-=- (simplified routing model). In our attempt to obtain an upper bound on the routing number of complete d-ary trees, we run into a problem of independent interest. This is the problem of heap construct... |

3 | Dynamic tree routing under the "matching with consumption" model - Pantziou, Roberts, et al. - 1996 |

2 | Packet routing via matchings. Unpublished manuscript - Krizanc, Zhang - 1996 |