## A Fully Dynamic Algorithm for Distributed Shortest Paths (2003)

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Venue: | Theoretical Computer Science |

Citations: | 9 - 6 self |

### BibTeX

@ARTICLE{Cicerone03afully,

author = {Serafino Cicerone and Gabriele Di Stefano and Daniele Frigioni and Umberto Nanni},

title = {A Fully Dynamic Algorithm for Distributed Shortest Paths},

journal = {Theoretical Computer Science},

year = {2003},

volume = {297},

pages = {1--3}

}

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### Abstract

We propose a fully-dynamic distributed algorithm for the all-pairs shortest paths problem on general networks with positive real edge weights. If is the number of pairs of nodes changing the distance after a single edge modi cation (insert, delete, weight decrease, or weight increase) then the message complexity of the proposed algorithm is O(n ) in the worst case, where n is the number of nodes of the network.

### Citations

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Network Flows: Theory, Algorithms, and Applications
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(Show Context)
Citation Context ...test paths in graphs is motivated by the numerous theoretical and practical applications known in variousselds as, for instance, in combinatorial optimization and in communication networks (e.g., see =-=[1, 13]-=-). We consider the distributed version of the all-pairs shortest paths problem. Finding ecient solutions for this problem is crucial when processors in a network need to route messages with the minimu... |

1145 |
Computer Networks
- Tanenbaum
- 2002
(Show Context)
Citation Context ...reason, the problem of updating shortest paths in a dynamic distributed environment arises naturally in practical applications. For instance, the OSPF protocol, widely used in the Internet (e.g., see =-=[11, 16]-=-), basically updates the routing tables of the nodes after a change to the network by using a distributed version of Dijkstra's algorithm. In this and many other crucial applications the worst case co... |

192 |
OSPF: Anatomy of an Internet Routing Protocol
- Moy
- 1998
(Show Context)
Citation Context ...reason, the problem of updating shortest paths in a dynamic distributed environment arises naturally in practical applications. For instance, the OSPF protocol, widely used in the Internet (e.g., see =-=[11, 16]-=-), basically updates the routing tables of the nodes after a change to the network by using a distributed version of Dijkstra's algorithm. In this and many other crucial applications the worst case co... |

72 |
Incremental evaluation of computational circuits
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- 1990
(Show Context)
Citation Context ... observed that the output complexity [5, 6, 13] was a good candidate. In fact, the output complexity has been shown to be a robust measure of performance for dynamic algorithms in the sequential case =-=[2, 5, 6, 13, 14]-=-. This notion applies when the algorithms operate within a framework where explicit updates are required on a given data structure. In such a framework, output complexity allows to evaluate the cost o... |

68 |
Incremental Algorithms for Minimal Length Paths
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- 1991
(Show Context)
Citation Context ...direction, in [9] an ecient incremental solution has been provided, and the diculty of dealing with edge deletions has been addressed. This diculty arises also in the sequential case (see for example =-=[3-=-]). In this paper, the second direction is investigated. Concerning the choice of a dierent complexity model, we observed that the output complexity [5, 6, 13] was a good candidate. In fact, the outpu... |

54 | On the computational complexity of dynamic graph problems - Ramalingam, Reps - 1996 |

51 |
Fully dynamic algorithms for maintaining shortest paths trees
- Frigioni, Marchetti-Spaccamela, et al.
(Show Context)
Citation Context ...ster than recomputing everything from scratch after each update, both for single-source and all-pairs shortest paths. Actually, only output bounded fully dynamic solutions are known on general graphs =-=[6, 14]-=-. Some attempts have been made also in the distributed case [4, 7, 9, 12, 15]. In thisseld the eciency of an algorithm is evaluated in terms of message, time and space complexity as follows. The messa... |

43 | Another Adaptive Distributed Shortest Path Algorithm
- Humblet
- 1991
(Show Context)
Citation Context ...when multiple edge changes occur simultaneously in the network. Several solutions of this problem rely on the classical Ford-Bellman method, originally introduced in the Arpanet [10]. For example, in =-=[8-=-] Humblet proposes a dierent solution, based on Dijkstra's algorithm for shortest paths, that overcomes some drawbacks of previous protocols. An interesting further research is to apply the new ideas ... |

36 |
Bounded incremental computation
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- 1977
(Show Context)
Citation Context ...test paths in graphs is motivated by the numerous theoretical and practical applications known in variousselds as, for instance, in combinatorial optimization and in communication networks (e.g., see =-=[1, 13]-=-). We consider the distributed version of the all-pairs shortest paths problem. Finding ecient solutions for this problem is crucial when processors in a network need to route messages with the minimu... |

33 |
Adaptive routing algorithms for distributed computer networks
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(Show Context)
Citation Context ...dating shortest paths when multiple edge changes occur simultaneously in the network. Several solutions of this problem rely on the classical Ford-Bellman method, originally introduced in the Arpanet =-=[10-=-]. For example, in [8] Humblet proposes a dierent solution, based on Dijkstra's algorithm for shortest paths, that overcomes some drawbacks of previous protocols. An interesting further research is to... |

23 |
On Finding and Updating Shortest Paths Distributively
- Ramarao, Venkatesan
- 1992
(Show Context)
Citation Context ...th for single-source and all-pairs shortest paths. Actually, only output bounded fully dynamic solutions are known on general graphs [6, 14]. Some attempts have been made also in the distributed case =-=[4, 7, 9, 12, 15]-=-. In thisseld the eciency of an algorithm is evaluated in terms of message, time and space complexity as follows. The message complexity of a distributed algorithm is the total number of messages sent... |

22 | Semi-dynamic algorithms for maintaining single source shortest paths trees
- Frigioni, Marchetti-Spaccamela, et al.
- 1998
(Show Context)
Citation Context ...es also in the sequential case (see for example [3]). In this paper, the second direction is investigated. Concerning the choice of a dierent complexity model, we observed that the output complexity [=-=5, 6, 13]-=- was a good candidate. In fact, the output complexity has been shown to be a robust measure of performance for dynamic algorithms in the sequential case [2, 5, 6, 13, 14]. This notion applies when the... |

16 |
Communication-Optimal Maintenance of Replicated Information
- Awerbuch, Cidon, et al.
- 1990
(Show Context)
Citation Context ...th for single-source and all-pairs shortest paths. Actually, only output bounded fully dynamic solutions are known on general graphs [6, 14]. Some attempts have been made also in the distributed case =-=[4, 7, 9, 12, 15]-=-. In thisseld the eciency of an algorithm is evaluated in terms of message, time and space complexity as follows. The message complexity of a distributed algorithm is the total number of messages sent... |

9 | An “All Pairs Shortest Paths” Distributed Algorithm Using 2n2 Messages - Haldar - 1997 |

9 |
Distributed Algorithms for Updating Shortest Paths
- Italiano
- 1991
(Show Context)
Citation Context ...th for single-source and all-pairs shortest paths. Actually, only output bounded fully dynamic solutions are known on general graphs [6, 14]. Some attempts have been made also in the distributed case =-=[4, 7, 9, 12, 15]-=-. In thisseld the eciency of an algorithm is evaluated in terms of message, time and space complexity as follows. The message complexity of a distributed algorithm is the total number of messages sent... |

6 |
Distributed shortest-path and minimum-delay protocols in networks with time-dependent edge-length
- Orda, Rom
- 1996
(Show Context)
Citation Context |