## Upper and Lower Bounds for Routing Schemes in Dynamic Networks (1989)

Venue: | Proc. 30th Symp. on Foundations of Computer Science |

Citations: | 23 - 0 self |

### BibTeX

@INPROCEEDINGS{Afek89upperand,

author = {Yehuda Afek and Eli Gafni and Moty Ricklin},

title = {Upper and Lower Bounds for Routing Schemes in Dynamic Networks},

booktitle = {Proc. 30th Symp. on Foundations of Computer Science},

year = {1989},

pages = {370--375},

publisher = {Society Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present an algorithm and two lower bounds for the problem of constructing and maintaining routing schemes in dynamic networks. The algorithm distributively assignes addresses to nodes and constructs routing tables in a dynamically growing tree. The resulting routing scheme routes data messages over the shortest path between any source and destination, assigns addresses of O(log^2 n) bits to each node, and uses in its routing tables O(log^3 n) bits of memory per incident link, where n is the final number of nodes in the tree. The amortized communication cost of the algorithm is O(log n) messages per node. We also give two lower bounds on the tradeoff between the quality of routing schemes (i.e., their stretch factor) and their amortized communication cost in general dynamic networks.

### Citations

134 |
Labelling and implicit routing in networks
- Santoro, Khatib
- 1985
(Show Context)
Citation Context ... address of a node is not in any of the explicit intervals then the messages for that node are routed over the default link. A simple ITR scheme which is based on Depth First Search (DFS) is given in =-=[SK85]-=-. In this scheme, the each time a data message is routed we might need to retrieve information from a slow memory [CGK88] thus dramatically effecting the delay of data messages in the network. nodes o... |

102 | F.: Hierarchical routing for large networks; performance evaluation and optimization - Kleinrock, Kamoun - 1977 |

72 | Compact distributed data structures for adaptive routing
- Awerbuch, Bar-Noy, et al.
- 1989
(Show Context)
Citation Context ...ks. These schemes should adapt to dynamically changing networks with low adaptation cost, while maintaining fixed addresses. (I.e., addresses should not change despite topological changes.) Following =-=[ABNLP88a]-=-, we consider the following measures and characteristics of routing schemes: ffl Stretch factor: The stretch factor of a routing scheme is the maximum over all node pairs (s; t) of the ratio between t... |

70 | Improved routing strategies with succinct tables - Awerbuch, Bar-Noy, et al. - 1990 |

69 |
Applying static network protocols to dynamic networks
- Afek, Awerbuch, et al.
- 1987
(Show Context)
Citation Context ... factor and adaptation cost of routing schemes for dynamic networks. In the first lower bound, we prove that any routing scheme in an arbitrary dynamic network (in which links may come up and go down =-=[AAG87]-=-), whose stretch factor is less than k must send\Omega\Gamma n=k) messages per topological change to update the routing functions at the various nodes. Second, we prove the same lower bound on routing... |

69 | Interval routing
- Leeuwen, Tan
- 1987
(Show Context)
Citation Context ... link is the range of dfs-numbers of its descendants. This scheme has stretch-factor 1, address size log n bits, and log n bits of memory per incident link to store the intervals. Van Leeuwen and Tan =-=[vLT87]-=- built on this idea to present a scheme for dynamically growing trees that does not preserve fixed addressing and has an O(n) adaptation cost per topological change. An ITR scheme for dynamically grow... |

38 |
A tradeoff between size and efficiency for routing tables
- Peleg, Upfal
- 1989
(Show Context)
Citation Context ...the last topological change. 2 (We assume 1 unit of cost for transmitting a message over any link.) ffl Space requirement: The maximum memory required to store the routing function at any node. 3 see =-=[PU88]-=-. 2 Clearly, at times of topological changes an adversary can force the routing schemes to behave poorly, e.g. with an \Omega\Gamma n) stretch factor. 3 The space requirement of a routing scheme is an... |

20 | Local management of a global resource in a communication network
- Afek, Awerbuch, et al.
- 1996
(Show Context)
Citation Context ... addressing and has an O(n) adaptation cost per topological change. An ITR scheme for dynamically growing trees that does preserve fixed addressing and has logarithmic adaptation cost is presented in =-=[AAPS87]-=-, where the problem of name assignment is considered. The resulting ITR scheme has stretch factor 1, address size at most O(log n) bits, but its space complexity is O(n \Delta log n) bits. In this pap... |

19 | Separator-based strategies for efficient message routing - Frederickson, Janardan - 1986 |

16 | Optimal clustering structures for hierarchical topological design of large computer networks - Kleinrock, Kamoun - 1980 |

7 | Detecting global termination conditions in the face of uncertainty - Afek, Saks - 1987 |

2 | Approximating the size of a dynamically growing distributed network - Awerbuch, Plotkin - 1987 |

1 | Memory-balanced routing strategies - Awerbuch, Bar-Noy, et al. - 1988 |

1 | Fault toletant leader election with termination detection, in general undirected networks - Bar-Yehuda, Kutten - 1986 |

1 |
New models and algorithms for future networks. Submitted
- Cidon, Gopal, et al.
- 1988
(Show Context)
Citation Context ...ink. A simple ITR scheme which is based on Depth First Search (DFS) is given in [SK85]. In this scheme, the each time a data message is routed we might need to retrieve information from a slow memory =-=[CGK88]-=- thus dramatically effecting the delay of data messages in the network. nodes of a rooted tree are numbered with depth-firstsearch numbers, and the interval of each link is the range of dfs-numbers of... |