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## Greedy Online Algorithms for Routing Permanent Virtual Circuits (1999)

Venue: | Networks |

Citations: | 1 - 0 self |

### Citations

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Bounds for certain multiprocessing anomalies, Bell Syst
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Citation Context ...the job's load vector. The goal of any algorithm is to minimize the maximum load on the machines. When machines are identical, the problem is the classical machine scheduling problem for which Graham =-=[15]-=- proved that the greedy algorithm which assigns each job to the machine with the least load is \Gamma 2 \Gamma 1 n \Delta competitive. Recently, new algorithms with constant (for all n) competitive ra... |

217 | Throughput-competitive on-line routing.
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Citation Context ...) of accepted requests. When durations are unknown, no competitive algorithm exists for the problem, even on a single link and even if preemption is allowed [13]. However, Awerbuch, Azar, and Plotkin =-=[5]-=- designed an admission control and routing algorithm for virtual circuits with known duration. As with Exp Route, the algorithm first assigns to each link a cost that is an exponential function of the... |

191 | Improved approximation algorithms for the multi-commodity flow problem and local competitive routing in dynamic networks.
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Citation Context ...ere exist better greedy algorithms. Aspnes, et al. [1, 2] designed an elegant, asymptotically optimal online algorithm, based on techniques to approximately solve offline multicommodity flow problems =-=[25, 21, 20], which -=-assigns to each request a shortest path with respect to the following exponential cost function: cost e (j) = a �� j (e)+ l j c(e) \Gamma a �� j (e) where a = 1 + fl for any 0 ! fl ! 1. This a... |

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The Maximum Concurrent Flow Problem”,
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Citation Context ...ere exist better greedy algorithms. Aspnes, et al. [1, 2] designed an elegant, asymptotically optimal online algorithm, based on techniques to approximately solve offline multicommodity flow problems =-=[25, 21, 20], which -=-assigns to each request a shortest path with respect to the following exponential cost function: cost e (j) = a �� j (e)+ l j c(e) \Gamma a �� j (e) where a = 1 + fl for any 0 ! fl ! 1. This a... |

110 | The competitiveness of on-line assignments.
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Citation Context ...os strictly less than two were designed by Bartal, Fiat, Karloff, and Vohra [12] and Karger, Phillips, and Torng [18]. For the identical machines with assignment restriction case, Azar, Naor, and Rom =-=[10, 11]-=- proved that the greedy algorithm is dlog ne + 1 competitive. They further showed that this bound is tight, up to an additive 1, by proving a lower bound of dlog(n + 1)e for any algorithm. They also d... |

105 | Competitive Non–Preemptive Call Control.
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- 1994
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Citation Context ...erived from this result [24]. Without the above assumptions, randomized online algorithms with polylogarithmic competitive ratios have been designed for trees, meshes, trees of meshes, and hypercubes =-=[7, 8, 22]-=-. For a distributed environment, Awerbuch and Azar [3] designed randomized online algorithms with polylogarithmic competitive ratios. The online permanent virtual circuit routing problem we consider i... |

103 |
On-line load balancing with applications to machine scheduling and virtual circuit routing
- Aspens, Azar, et al.
- 1993
(Show Context)
Citation Context ...the number of network nodes and d is the length of the longest path that can be assigned to a request. It is known that the optimal competitive ratio for this problem is \Theta(log n). Aspnes, et al. =-=[1, 2]-=- designed a \Theta(log n) competitive online algorithm that computes an exponential function of current congestion to make each decision. The greedy online algorithms, although not optimal, make each ... |

97 | New algorithms for an ancient scheduling problem.
- Bartal, Fiat, et al.
- 1995
(Show Context)
Citation Context ...he least load is \Gamma 2 \Gamma 1 n \Delta competitive. Recently, new algorithms with constant (for all n) competitive ratios strictly less than two were designed by Bartal, Fiat, Karloff, and Vohra =-=[12]-=- and Karger, Phillips, and Torng [18]. For the identical machines with assignment restriction case, Azar, Naor, and Rom [10, 11] proved that the greedy algorithm is dlog ne + 1 competitive. They furth... |

91 | Competitive routing of virtual circuits in ATM networks - Plotkin - 1995 |

88 | Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts.
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- 1994
(Show Context)
Citation Context ...ere exist better greedy algorithms. Aspnes, et al. [1, 2] designed an elegant, asymptotically optimal online algorithm, based on techniques to approximately solve offline multicommodity flow problems =-=[25, 21, 20], which -=-assigns to each request a shortest path with respect to the following exponential cost function: cost e (j) = a �� j (e)+ l j c(e) \Gamma a �� j (e) where a = 1 + fl for any 0 ! fl ! 1. This a... |

82 | On-line routing of virtual circuits with applications to load balancing and machine scheduling.
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- 1997
(Show Context)
Citation Context ...d networks. These results answer open questions posed by Mao and Simha [23] and also present alternatives to the asymptotically optimal, but computationally more expensive algorithm of Aspnes, et al. =-=[1, 2]-=-. We discussed situations in which the greedy algorithms can be expected to perform well in Sections 2 and 3. Since there is a tradeoff between speed and efficiency in the choice of algorithms, the de... |

65 | Competitive routing of virtual circuits with unknown duration
- Awerbuch, Azar, et al.
- 1994
(Show Context)
Citation Context ... factor of 4 increase in the competitive ratio. a virtual circuit, by concurrently using this algorithm to solve one instance of permanent virtual circuit routing for each time step. Awerbuch, et al. =-=[6]-=- noted that the competitive ratio of any online algorithm for routing switched virtual circuits with unknown durations must be\Omega ( 4 p n). However, they designed a O(log n) competitive algorithm t... |

65 | On-line admission control and circuit routing for high performance computing and communication
- Awerbuch, Gawlick, et al.
- 1994
(Show Context)
Citation Context ...erived from this result [24]. Without the above assumptions, randomized online algorithms with polylogarithmic competitive ratios have been designed for trees, meshes, trees of meshes, and hypercubes =-=[7, 8, 22]-=-. For a distributed environment, Awerbuch and Azar [3] designed randomized online algorithms with polylogarithmic competitive ratios. The online permanent virtual circuit routing problem we consider i... |

63 | A better algorithm for an ancient scheduling problem,
- Karger, Phillips, et al.
- 1996
(Show Context)
Citation Context ...\Delta competitive. Recently, new algorithms with constant (for all n) competitive ratios strictly less than two were designed by Bartal, Fiat, Karloff, and Vohra [12] and Karger, Phillips, and Torng =-=[18]-=-. For the identical machines with assignment restriction case, Azar, Naor, and Rom [10, 11] proved that the greedy algorithm is dlog ne + 1 competitive. They further showed that this bound is tight, u... |

56 | Online load balancing of temporary tasks
- Azar, Kalyanasundaram, et al.
- 1997
(Show Context)
Citation Context ...g that no algorithm can have a competitive ratio better than log n\Gamma1 2 . An alternative proof, showing a lower bound of log n+3 2 , was given in [17]. For switched virtual circuits, Azar, et al. =-=[9]-=- showed how to derive a O(log(nT )) competitive algorithm, where T is the maximum duration of 1 This is technically only true if the optimal congestion is 1. For the more general case, the algorithm m... |

47 |
On-line algorithms versus off-line algorithms: How much is it worth to know the future?
- Karp
- 1992
(Show Context)
Citation Context ...e if it always finds a solution whose cost, or objective function value, is within a small factor of the cost incurred by an optimal offline algorithm. This technique is known as competitive analysis =-=[19]-=-. Intuitively, competitive analysis measures the degree to which the performance of an online algorithm suffers, due to its lack of knowledge about the future, compared to that of an optimal offline a... |

46 |
Connection preemption in communication networks,”
- Garay, Gopal
- 1992
(Show Context)
Citation Context ...e throughput (or more generally, the profit) of accepted requests. When durations are unknown, no competitive algorithm exists for the problem, even on a single link and even if preemption is allowed =-=[13]-=-. However, Awerbuch, Azar, and Plotkin [5] designed an admission control and routing algorithm for virtual circuits with known duration. As with Exp Route, the algorithm first assigns to each link a c... |

38 | Local optimization of global objectives: competitive distributed deadlock resolution and resource allocation
- Awerbuch, Azar
- 1994
(Show Context)
Citation Context ...randomized online algorithms with polylogarithmic competitive ratios have been designed for trees, meshes, trees of meshes, and hypercubes [7, 8, 22]. For a distributed environment, Awerbuch and Azar =-=[3]-=- designed randomized online algorithms with polylogarithmic competitive ratios. The online permanent virtual circuit routing problem we consider is a generalization of an online load balancing problem... |

29 | On–line Randomized Call–Control Revisited.
- Leonardi, Marchetti–Spaccamela, et al.
- 1998
(Show Context)
Citation Context ...erived from this result [24]. Without the above assumptions, randomized online algorithms with polylogarithmic competitive ratios have been designed for trees, meshes, trees of meshes, and hypercubes =-=[7, 8, 22]-=-. For a distributed environment, Awerbuch and Azar [3] designed randomized online algorithms with polylogarithmic competitive ratios. The online permanent virtual circuit routing problem we consider i... |

16 |
On-line routing for permanent virtual circuits
- Gawlick, Kalmanek, et al.
- 1995
(Show Context)
Citation Context ...nks. Taking this into account, the factor of d in the competitive ratio of Greedy Route2 makes intuitive sense. We should mention that Greedy Route2 is identical to the min-max algorithm simulated in =-=[14]-=-, and compared to the min-hop algorithm and a variant of Exp Route. In these simulations the goal was to maximize throughput rather than minimize congestion. Greedy Route2 was shown to route up to 25%... |

10 | Packet routing via min-cost circuit routing
- Awerbuch, Azar, et al.
- 1996
(Show Context)
Citation Context ...h congestion ��s1. We point out that this modified definition of competitive, which limits consideration to a subset of instances, namely feasible instances, has appeared previously in the literat=-=ure [4]-=-. Corollary 1 The competitive ratio of Greedy Route1 is O i p Dm j if any of the following are true: (a) L = O(1); (b) the set of optimal routes is pairwise edge disjoint; (c) the request sequence is ... |

7 | A lower bound for on-line file transfer routing and scheduling
- Havill, Mao, et al.
- 1997
(Show Context)
Citation Context ...ute is optimal (up to a constant factor) by showing that no algorithm can have a competitive ratio better than log n\Gamma1 2 . An alternative proof, showing a lower bound of log n+3 2 , was given in =-=[17]-=-. For switched virtual circuits, Azar, et al. [9] showed how to derive a O(log(nT )) competitive algorithm, where T is the maximum duration of 1 This is technically only true if the optimal congestion... |

6 | Routing and scheduling file transfers in packetswitched networks
- Mao, Simha
- 1994
(Show Context)
Citation Context ... at least three related threads of research that relate to the online routing problem we consider. We will first describe these results and then explain how our contribution is related. Mao and Simha =-=[23]-=- studied three simple online list scheduling (LS) algorithms for permanent virtual circuit routing. The three online routing algorithms are described as follows: Algorithm LS1 For request f j , assign... |

1 |
Greedy on-line file transfer routing
- Havill, Mao
- 1997
(Show Context)
Citation Context ...ompetitive ratio for this problem is \Theta(log n) with respect This research was supported in part by NSF grant NCR-9505963. A preliminary version of the some of the results in Section 3 appeared in =-=[16]-=-. to network congestion, where n is the number of network nodes. Aspnes, et al. [1, 2] designed an optimal O(log n) competitive online algorithm that computes an exponential function of current conges... |