## Computing Shortest Paths for Any Number of Hops (1998)

Citations: | 27 - 2 self |

### BibTeX

@MISC{Guerin98computingshortest,

author = {Roch Guerin and Ariel Orda},

title = {Computing Shortest Paths for Any Number of Hops},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we introduce and investigate a #new" path optimization problem which we denote as the All Hops Optimal Path #AHOP# problem. The problem involves identifying, for all hop counts, the optimal, i.e., minimum weight, path between a given source and destination. Our interest in such a problem originated in the context of Quality-of-Service #QoS# routing in networks. A goal of QoS routing is to improve a network's ability to satisfy user requirements by selecting paths for individual requests, which are based on both the network state and the request requirements, e.g., minimum bandwidth or maximum end-to-end delay constraints. In addition, in order to ensure e#cient network operation, it is desirable that the paths also use the minimum possible amount of network resources, e.g., minimize the number of links #hops# used. As a results of these additional constraints, the path selection computation increases in complexity, and it becomes important to amortize this incre...

### Citations

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Citation Context ...) constraints, while minimizing the network cost function. This corresponds to a standard optimal path selection under constraints that has been widely studied in many different settings (see [2] and =-=[3]-=- for a general discussion and presentation of numerous algorithms). The problem in its most general form, i.e., multiple additive constraints, is known to be NP-complete [4], and, as a result, much ef... |

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Citation Context ...vantage of substituting additive metrics with bottleneck metrics. For example, certain (rate-based) schedulers often enable mapping delay constraints onto rate constraints (see, e.g., [17], [5], [6], =-=[18]-=-–[20]), hence, our results may provide additional support for their deployment. GUÉRIN AND ORDA: COMPUTING SHORTEST PATHS FOR ANY NUMBER OF HOPS 619 APPENDIX PSEUDOCODE OF ALGORITHM IBF This Appendix ... |

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Citation Context ...(service) constraints, while minimizing the network cost function. This corresponds to a standard optimal path selection under constraints that has been widely studied in many different settings (see =-=[2]-=- and [3] for a general discussion and presentation of numerous algorithms). The problem in its most general form, i.e., multiple additive constraints, is known to be NP-complete [4], and, as a result,... |

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Citation Context ...S and Traffic Engineering, contain ample evidences of associated activities and numerous pointers to relevant publications, RFCs, and Internet Drafts. over paths that are capable of meeting them (see =-=[1]-=- for a comprehensive survey). Furthermore, for efficiency purposes, it is also important to do so at the minimum possible cost to the network. From an algorithmic standpoint, this calls for algorithms... |

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Citation Context ...idence on the advantage of substituting additive metrics with bottleneck metrics. For example, certain (rate-based) schedulers often enable mapping delay constraints onto rate constraints (see, e.g., =-=[17]-=-, [5], [6], [18]–[20]), hence, our results may provide additional support for their deployment. GUÉRIN AND ORDA: COMPUTING SHORTEST PATHS FOR ANY NUMBER OF HOPS 619 APPENDIX PSEUDOCODE OF ALGORITHM IB... |

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Citation Context ...uss later, and this makes them attractive from a computational standpoint. As a result, computing minimum hop paths with service constraints has become a recurring problem in data networks, e.g., see =-=[7]-=- and [8] for recent examples and proposals. The extension from this single minimum hop path computation to the AHOP problem, originates from the need to amortize the associated computational cost over... |

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Citation Context ...ge of substituting additive metrics with bottleneck metrics. For example, certain (rate-based) schedulers often enable mapping delay constraints onto rate constraints (see, e.g., [17], [5], [6], [18]–=-=[20]-=-), hence, our results may provide additional support for their deployment. GUÉRIN AND ORDA: COMPUTING SHORTEST PATHS FOR ANY NUMBER OF HOPS 619 APPENDIX PSEUDOCODE OF ALGORITHM IBF This Appendix provi... |

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Citation Context ... number of “special” cost functions that are of interest in data networks, not only because they provide practical cost measures, but also because they are amenable to tractable solutions (see, e.g., =-=[5]-=-, [6]). In particular, the number (count) of hops in a path is both a realistic and popular measure of cost. Hop count accurately captures network cost as it measures the number of links over which ne... |

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Citation Context ...ms, in particular Dijkstra’s and Bellman–Ford’s, fit into this class; this is the case also with many other algorithms, e.g., [12], [13]. However, some algorithms are not path-comparison-based, e.g., =-=[14]-=-, as it adds weights of edges that do not form a single path. The latter belongs to a class of “algebraic” algorithms that consider shortest paths from the perspective of matrix multiplication. We not... |

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Citation Context ...among a certain class of path-comparison-based algorithms, which includes standard solutions such as Dijkstra’s and Bellman–Ford’s. The proof is based on an extension of a similar result, obtained in =-=[11]-=- for the all-pairs shortest path problem, and establishes the optimality of a BF-based solution for additive metrics. However, for bottleneck metrics, we show that a lower complexity solution is avail... |

59 | Implementation and Performance Measurements of QoS Routing Extensions to OSPF
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Citation Context ...t over multiple path requests. This is because even if the algorithms involved are tractable, performing them repeatedly for every new request can translate into a significant computational load (see =-=[9]-=- for an experimental investigation). One option for minimizing this overhead is to precompute minimum cost (hop count) paths for all possible requests. Assuming that this is feasible, such a precomput... |

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Citation Context ...efore, a potential topic for future research is to devise a solution for the AHOP problem under bottleneck metrics which would improve upon the basic BF solution in the case of sparse topologies; see =-=[15]-=- for related results. More generally, it would be interesting to obtain a lower bound for the AHOP problem under bottleneck metrics, in both cases of general and sparse topologies, and, in addition, t... |

25 |
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Citation Context ... encoding of the solution. Most commonly used shortest-path algorithms, in particular Dijkstra’s and Bellman–Ford’s, fit into this class; this is the case also with many other algorithms, e.g., [12], =-=[13]-=-. However, some algorithms are not path-comparison-based, e.g., [14], as it adds weights of edges that do not form a single path. The latter belongs to a class of “algebraic” algorithms that consider ... |

24 |
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Citation Context ...er of “special” cost functions that are of interest in data networks, not only because they provide practical cost measures, but also because they are amenable to tractable solutions (see, e.g., [5], =-=[6]-=-). In particular, the number (count) of hops in a path is both a realistic and popular measure of cost. Hop count accurately captures network cost as it measures the number of links over which network... |

12 |
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(Show Context)
Citation Context ...hop count) paths for all possible requests. Assuming that this is feasible, such a precomputation can then be performed only occasionally, e.g., as the state of the network changes significantly (see =-=[10]-=- for a discussion of this issue), and the precomputed paths are reused each time a new request is made. 1063-6692/02$17.00 © 2002 IEEE 614 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 10, NO. 5, OCTOBER ... |

7 | QoS Routing Mechanisms and OSPF Extensions. Request for Comments 2676, Internet Engineering Task Force - Apostolopoulos, Kama, et al. - 1999 |

4 | Server based QoS routing - Apostolopoulos, Guerin, et al. - 1999 |

3 |
QoS routing mechanisms and
- Apostolopoulos, Williams, et al.
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(Show Context)
Citation Context ...r, and this makes them attractive from a computational standpoint. As a result, computing minimum hop paths with service constraints has become a recurring problem in data networks, e.g., see [7] and =-=[8]-=- for recent examples and proposals. The extension from this single minimum hop path computation to the AHOP problem, originates from the need to amortize the associated computational cost over multipl... |

1 |
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Citation Context ...unts and destinations, but also all possible sources. This is motivated by the fact that a route server would be faced with such a task. Route servers are potentially important in practice, e.g., see =-=[16]-=-, as they allow the deployment of new QoS routing algorithms with minimal impact, i.e., upgrade requirements, on the existing infrastructure. On a more general level, the results obtained for IBF indi... |