## Shortest-Path And Minimum-Delay Algorithms In Networks With Time-Dependent Edge-Length (1990)

### Cached

### Download Links

- [www.inf.fu-berlin.de]
- [cs.ucsb.edu]
- [ftp.technion.ac.il]
- DBLP

### Other Repositories/Bibliography

Venue: | Journal of the ACM |

Citations: | 99 - 6 self |

### BibTeX

@ARTICLE{Orda90shortest-pathand,

author = {Ariel Orda and Raphael Rom},

title = {Shortest-Path And Minimum-Delay Algorithms In Networks With Time-Dependent Edge-Length},

journal = {Journal of the ACM},

year = {1990},

volume = {37},

pages = {607--625}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider in this paper the shortest-path problem in networks in which the delay (or weight) of the edges changes with time according to arbitrary functions. We present algorithms for finding the shortest-path and minimum-delay under various waiting constraints and investigate the properties of the derived path. We show that if departure time from the source node is unrestricted then a shortest path can be found that is simple and achieves a delay as short as the most unrestricted path. In the case of restricted transit, it is shown that there exist cases where the minimum delay is finite but the path that achieves it is infinite. ____________________________________ This research was supported by the Foundation for Research in Electronics, Computers and Communications, Administered by the Israel Academy of Science and Humanities I. INTRODUCTION Shortest paths algorithms have been the subject of extensive research for many years resulting in a large number of algorithms for vario...

### Citations

888 |
A note on two problems in connection with graphs, Numerische Mathematik 1
- Dijkstra
- 1959
(Show Context)
Citation Context ...time t S we look for shortest paths and minimum delays between s and all other nodes for that starting time. As noted in Dreyfus[8] this is a straightforward extension to such algorithms as Dijkstra's=-=[12]-=- or Ford's[6]. We present the algorithm here to become familiar with some notions and differences from the standard version that will be helpful later. We start by making some observations regarding o... |

822 |
Flows in Networks
- Fulkerson
- 1962
(Show Context)
Citation Context ...for shortest paths and minimum delays between s and all other nodes for that starting time. As noted in Dreyfus [4], this is a straightforward extension to such algorithms as Dijkstra’s [3] or Ford’s =-=[8]-=-. We present the algorithm here to become familiar with some notions and differences from the standard version that will be helpful later. We start by making some observations regarding optimal waitin... |

354 |
Graph Algorithms
- Even
- 1979
(Show Context)
Citation Context ...l delay function (including optimal waiting) for the delay function of Figure 1. from s to any node j is a shortest topological path for starting time ts whose delay is given by Xj - ts . PROOF. Even =-=[5]-=-). The proof follows closely that of Dijkstra’s algorithm (see, for example, Cl COROLLARY 1. In the UW model, for any source-destination pair and any starting time, there exists a simple and concatena... |

276 | The new routing algorithm for the ARPANET
- McQuillan, Richer, et al.
- 1980
(Show Context)
Citation Context ...nally become unavailable (i.e., infinite weight) and others deal with quasi static models, that is, link weights that change from time to time but remain constant in between these (infrequent) changes=-=[2,3]-=-. Time dependent shortest path problems have been studied for the case of discrete delay functions whose domain and range are the positive integers. Such problems were addressed both directly [4,5] an... |

143 |
Distributed network protocols
- Segall
- 1983
(Show Context)
Citation Context ...ns of network control algorithms. Indeed, for the static or quasi-static environment, several distributed shortest path algorithms were developed based on centralized versions. (See for example Segall=-=[14]). Such di-=-stributed versions were developed and investigated also for the algorithms presented in this paper[15]. This paper considers minimum-delay paths. In a general case, the "length" of a link ma... |

120 |
An appraisal of some shortest path algorithms
- Dreyfus
- 1969
(Show Context)
Citation Context ...shortest path problem without these restrictions, i.e., we allow arbitrary functions for link delays. In this respect this is the broadest generalization. Such a problem was briefly treated by Dreyfus=-=[8]-=- and Ling et.al.[9] which address only limited cases. The most direct treatment to date was done by Halpern[10] where arbitrary waiting times are also considered. In this latter work an algorithm is p... |

111 |
Flow control: a comparative survey
- Gerla, Kleinrock
- 1980
(Show Context)
Citation Context ...g (SW) in which waiting is disallowed everywhere along the message path through the network except at the source node which permits unlimited waiting. Note that waiting time is a means of flow control=-=[11]-=-. The UW model implies a hop-by-hop flow control, the SW an end-to-end flow control mechanism, and the FW rules out flow control. We now define the terminology used in analyzing the above models. Cons... |

85 |
Graph Algorithms, Computer Science
- Even
- 1979
(Show Context)
Citation Context ...path from s to any node j is a shortest topological path for starting time t S whose delay is given by X j - t S . Proof: The proof follows closely that of Dijkstra's algorithm (see, for example, Even=-=[13]-=-). Corollary 1: In the UW model, for any source-destination pair and any starting time, there exists a simple and concatenated shortest path. Note that optimal waiting times are implicitly given via t... |

70 |
Constructing maximal dynamic flows from static flows
- Ford, Fulkerson
- 1958
(Show Context)
Citation Context ...e been studied for the case of discrete delay functions whose domain and range are the positive integers. Such problems were addressed both directly [4,5] and indirectly in the context of maximal flow=-=[6,7]-=-. In this paper we address the shortest path problem without these restrictions, i.e., we allow arbitrary functions for link delays. In this respect this is the broadest generalization. Such a problem... |

66 |
The Shortest Route Through a Network with Time-Dependent Intermodal Transit Times
- Cooke, Halsey
- 1966
(Show Context)
Citation Context ...ges[2,3]. Time dependent shortest path problems have been studied for the case of discrete delay functions whose domain and range are the positive integers. Such problems were addressed both directly =-=[4,5]-=- and indirectly in the context of maximal flow[6,7]. In this paper we address the shortest path problem without these restrictions, i.e., we allow arbitrary functions for link delays. In this respect ... |

62 |
Shortest-path algorithms: Taxonomy and annotation
- Deo, Pang
- 1984
(Show Context)
Citation Context ...nce and Humanities I. INTRODUCTION Shortest paths algorithms have been the subject of extensive research for many years resulting in a large number of algorithms for various conditions and constraints=-=[1]-=-. The vast majority of these deal with fixed graphs i.e., fixed topology and fixed link weights. The advancement of computer networks and distributed processing has brought renewed interest in the sub... |

45 |
Updating Distances in Dynamic Graphs
- Even, Gazit
- 1985
(Show Context)
Citation Context ...nally become unavailable (i.e., infinite weight) and others deal with quasi static models, that is, link weights that change from time to time but remain constant in between these (infrequent) changes=-=[2,3]-=-. Time dependent shortest path problems have been studied for the case of discrete delay functions whose domain and range are the positive integers. Such problems were addressed both directly [4,5] an... |

33 | Minimum weight paths in time-dependent networks
- Orda, Rom
- 1991
(Show Context)
Citation Context ...han the minimum-delay one to the extent that the least restricted UW model does not guarantee the existence of simple, concatenated, or even finite optimal paths. The interested reader is referred to =-=[16] for discu-=-ssion and analysis of this problem. APPENDIX A Proof of Theorem 2 We start with some notations. Denote each execution of step 3 of algorithm UW2 as an "iteration". Let VAR n be the value of ... |

21 |
Shortest route with time dependent length of edges and limited delay possibilities in nodes
- Halpern
- 1977
(Show Context)
Citation Context ...respect this is the broadest generalization. Such a problem was briefly treated by Dreyfus[8] and Ling et.al.[9] which address only limited cases. The most direct treatment to date was done by Halpern=-=[10]-=- where arbitrary waiting times are also considered. In this latter work an algorithm is proposed for various waiting constraints, but this algorithm cannot be bounded by network topology (i.e., the nu... |

10 |
Determination of shortest path in a network with time-dependent edgelengths. Mathematische Operationsforschung und Statistik
- KLAFSZKY
- 1972
(Show Context)
Citation Context ...ges[2,3]. Time dependent shortest path problems have been studied for the case of discrete delay functions whose domain and range are the positive integers. Such problems were addressed both directly =-=[4,5]-=- and indirectly in the context of maximal flow[6,7]. In this paper we address the shortest path problem without these restrictions, i.e., we allow arbitrary functions for link delays. In this respect ... |

10 |
Shortest-Path Algorithms
- Deo, Pang
- 1984
(Show Context)
Citation Context ...nce and HumanitiesI. INTRODUCTION Shortest paths algorithms have been the subject of extensive research for many years resulting in a large number of algorithms for various conditions and constraints=-=[1]-=-. The vast majority of these deal with fixed graphs i.e., fixed topology and fixed link weights. The advancement of computer networks and distributed processing has brought renewed interest in the sub... |

7 | Distributed shortest-path protocols for time-dependent networks
- Orda, Rom
- 1988
(Show Context)
Citation Context ...st path algorithms were developed based on centralized versions. (See for example Segall[14]). Such distributed versions were developed and investigated also for the algorithms presented in this paper=-=[15]. This pap-=-er considers minimum-delay paths. In a general case, the "length" of a link may be characterized by factors other than delay such as reliability, traversal cost, etc. Since these factors may... |

2 |
Optimal path in networks with time-varying traverse time and expenses branches
- LING, FURUNO, et al.
- 1972
(Show Context)
Citation Context ...em without these restrictions, i.e., we allow arbitrary functions for link delays. In this respect this is the broadest generalization. Such a problem was briefly treated by Dreyfus[8] and Ling et.al.=-=[9]-=- which address only limited cases. The most direct treatment to date was done by Halpern[10] where arbitrary waiting times are also considered. In this latter work an algorithm is proposed for various... |

1 |
Distributed network protocols. IEEE Trans. on If: Theory
- SEGALL
- 1983
(Show Context)
Citation Context ...rsions of network control algorithms. Indeed, for the static or quasi-static environment, several distributed shortest path algorithms were developed based on centralized versions. (See, e.g., Segall =-=[16]-=-.) Such distributed versions were developed and investigated also for the algorithms presented in this paper [ 141. This paper considers minimum-delay paths. In a general case, the “length” of a link ... |