## Routing in Distributed Networks: Overview and Open Problems (2001)

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Venue: | ACM SIGACT News - Distributed Computing Column |

Citations: | 51 - 13 self |

### BibTeX

@ARTICLE{Gavoille01routingin,

author = {Cyril Gavoille},

title = {Routing in Distributed Networks: Overview and Open Problems},

journal = {ACM SIGACT News - Distributed Computing Column},

year = {2001},

volume = {32},

pages = {36--52}

}

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### Abstract

This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems.

### Citations

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Citation Context ...ior eciency-space tradeo. The hierarchical routing strategy presented in [4] uses O(k n 1=k log n) bits of local memory and guarantees a stretch factor O(k 2 9 k ). The routing strategy presented in [=-=6-=-] retains the advantages of the former one, while regaining the polynomial trade-o. In particular it guarantees, for every integer k > 1, a stretch factor of O(k 2 ), while using O(k n 1=k log 2 n log... |

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112 | Compact routing with minimum stretch
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Citation Context ...cted, but with a relatively low routing time). That is why, other routing strategies have been designed, in particular some routing strategies with small stretch factor s 2 [2; 5]. In this framework, =-=[10]-=- proposed direct loop-free routing schemes for weighted graphs with O(n 2=3 log 4=3 n) local memory space. The stretch is at most s = 3, and addresses and headers are of size 3 log n. The space bound ... |

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Citation Context ... to modify h0 , and to create thesrst header h1 of shorter size. 5 Other methods that overcome these problems achieve an inferior eciency-space tradeo. The hierarchical routing strategy presented in [=-=4]-=- uses O(k n 1=k log n) bits of local memory and guarantees a stretch factor O(k 2 9 k ). The routing strategy presented in [6] retains the advantages of the former one, while regaining the polynomial ... |

73 | Designing networks with compact routing tables - FREDERICKSON, JANARDAN - 1988 |

69 | Membership in constant time and almost minimum space
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Citation Context ...usly, the ideal solution would be a compact representation of the set fa 1 ; : : : ; a d g by a data structure of size 12 log n d = (d log(n=d)) allowing constant routing time. In the same spirit, [8=-=-=-] proposed a quasi-optimal coding of integer sets (up to a multiplicative constant) with constant time for membership queries. The question of computing the rank of an element is open. Open question ... |

64 | Space-efficiency for routing schemes of stretch factor three - Gavoille, Gengler |

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Citation Context ...y space. The stretch is at most s = 3, and addresses and headers are of size 3 log n. The space bound can be reduced to O( p n log 3=2 n) bits if one accept a small increasing on the stretch to s = 5 =-=[12]-=-. The latter routing strategy is based on routing tables (the tables are compacted into intervals of integers, namely these are interval routing schemes, cf. [21] for a survey of this technique). Thus... |

59 | Optimal interval routing - Fraigniaud, Gavoille - 1994 |

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Citation Context ... such kind of results are probabilities, with the family G n;p of random graphs 10 , or the Kolmogorov Complexity [29] with the Kolmogorov random graphs. These two tools are very close in essence. In =-=[13]-=- the ability of random graphs in G n;p , for some particular values of p, to support shortest path routing tables that can be compacted into intervals has been considered. More generally, and using Ko... |

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Citation Context ...phs whose adjacency matrix is not compressible in the Kolmogorov Complexity sense. 10 In this model, graphs have n nodes and with probability p there is an edge connecting two nodes of the graph, cf. =-=[7-=-]. 7 Open question Is the n + o(n) upper bound is the best possible one for a fraction of 1 o(1) of all the graphs? Remark. To design such a lower bound on the memory space is harder than it looks. F... |

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Citation Context ...e it adaptive to dynamic networks. It is willing that this maintaining algorithm has low message or time complexity. For more details on the dynamic case, we invite the reader to consult [1, 11], and =-=[2, 5, 28]-=- for endto -end communication problems, where the goal is to guarantee communications between asxed pair of nodes in spite of link failures with the minimum memory space in the nodes and minimum commu... |

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Citation Context ...me and to make it adaptive to dynamic networks. It is willing that this maintaining algorithm has low message or time complexity. For more details on the dynamic case, we invite the reader to consult =-=[1, 11]-=-, and [2, 5, 28] for endto -end communication problems, where the goal is to guarantee communications between asxed pair of nodes in spite of link failures with the minimum memory space in the nodes a... |

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Citation Context ...me and to make it adaptive to dynamic networks. It is willing that this maintaining algorithm has low message or time complexity. For more details on the dynamic case, we invite the reader to consult =-=[1, 11]-=-, and [2, 5, 28] for endto -end communication problems, where the goal is to guarantee communications between asxed pair of nodes in spite of link failures with the minimum memory space in the nodes a... |

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Citation Context ...e it adaptive to dynamic networks. It is willing that this maintaining algorithm has low message or time complexity. For more details on the dynamic case, we invite the reader to consult [1, 11], and =-=[2, 5, 28]-=- for endto -end communication problems, where the goal is to guarantee communications between asxed pair of nodes in spite of link failures with the minimum memory space in the nodes and minimum commu... |

23 | Sparse communication networks and efficient routing in the plane - Hassin, Peleg |

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5 |
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Citation Context ...en the header is empty. The total routing time on a route of length L is O(L+ log n), the log n term coming from the computation of thesrst header that can be performed by the Boyer-Moore's algorithm =-=[3]-=-. Note that the routing time is constant excepted in the source. Since L 6 log n (the diameter is k), the total routing time never exceeds O(log n). The problem to design a compact data structure in o... |

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4 |
anyi, Space-ecient routing tables for almost all networks and the incompressibility method
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Citation Context ...raphs in G n;p , for some particular values of p, to support shortest path routing tables that can be compacted into intervals has been considered. More generally, and using Kolmogorov random graphs, =-=[9]-=- showed that a fraction of at least 1 1=n 3 of all the graphs has a shortest path routing table of size 3n + o(n) bits (per node) under the assumption that node address range is [1; n] and node addres... |

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