Packet routing and job-shop scheduling inO(congestion+dilation) steps

Leighton, Frank Thomson; Maggs, Bruce M.; Rao, S. Srinivasa

doi:10.1007/bf01215349

Cited by 271 publications

(297 citation statements)

References 4 publications

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“…Showing how to modify Beck's arguments so that they can be applied to scheduling problems is the main contribution of the paper. Once this is done, the construction of optimal routing schedules is accomplished using the methods of [9].…”

Section: Our Resultsmentioning

confidence: 99%

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Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules,

Leighton¹,

Maggs²,

Richa³

1996

Self Cite

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In 1988, Leighton, Maggs, and Rao showed that for any network and any set of packets whose paths through the network are xed and edge-simple, there exists a schedule for routing the packets to their destinations in O(c + d) steps using constant-size queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lov asz Local Lemma and was not constructive. In this paper, we show h o w to nd such a s c hedule in O(P(loglog P) log P) time, with probability 1 1 = P , for any positive constant , where P is the sum of the lengths of the paths taken by the packets in the network.We also show h o w to parallelize the algorithm so that it runs in NC. The method that we use to construct the schedules is based on the algorithmic form of the Lov asz Local Lemma discovered by Beck.

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Section: Our Resultsmentioning

confidence: 99%

“…In [9], Leighton, Maggs, and Rao showed that there are much better schedules. In particular, they established the existence of a schedule using O(c + d) steps and constant-size queues at every edge, thereby achieving the naive l o w er bounds for any routing problem.…”

Section: Previous and Related Workmentioning

confidence: 99%

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules,

Leighton¹,

Maggs²,

Richa³

1996

Self Cite

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“…However, in these works, the authors consider the setting where all the packets have the same length, and they mainly give centralized algorithms. Randomized distributed or online algorithms have been proposed in [1,9,11], but in these algorithms the policy of each link does not only depend on the packets that are allocated to this link, but also on the total number of packets in the network.…”

Section: Related Workmentioning

confidence: 99%

“…The packet routing problem in general store-and-forward networks is an NP-hard problem [14] which has been extensively studied in the literature (see for example [1,9,10,11]). However, in these works, the authors consider the setting where all the packets have the same length, and they mainly give centralized algorithms.…”

Section: Related Workmentioning

confidence: 99%

The impact of local policies on the quality of packet routing in paths, trees, and rings

Angel

Bampis

Pascual

2008

J Sched

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We consider the packet routing problem in store-and-forward networks whose topologies are either paths, trees, or rings. We are interested by the quality of the solution produced, with respect to a global optimal solution, if each link uses a (fixed) local policy to schedule the packets which go through it. The quality of the derived solutions is measured using the worst case analysis for two global optimality criteria, namely the maximum arrival date of a packet at its destination (or makespan) and the average arrival date of the packets at their destinations.We consider the setting where n packets, each one having a size (or length) and a destination, are released from the same source. In the case of rings, there exist two paths between the source and a destination. Each packet is owned by a user which chooses a path to its destination. We assume that users are rational: knowing the local policy used by the links and the state of the network, a user chooses the path which minimizes the arrival date of its packet at its destination. We are then interested by the quality of the Nash equilibria obtained.

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“…A basic difference between those routing models and direct routing is that the packets don't follow some specific path. Optimal routing for given paths on arbitrary networks have been studied extensively in the context of store-and-forward algorithms (which are algorithms with buffers) [18,19,22,24,26].…”

Section: Related Workmentioning

confidence: 99%

Direct routing: Algorithms and complexity

et al. 2006

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Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing:(i) Algorithms. We present a polynomial time greedy direct algorithm which is worstcase optimal. We improve the bound of the greedy algorithm for special cases, by applying variants of the this algorithm to commonly used network topologies. In particular, we obtain near-optimal routing time for the tree, mesh, butterfly and hypercube.(ii) Complexity. By a reduction from Vertex Coloring, we show that optimal Direct Routing is inapproximable, unless P=NP.(iii) Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; in order to solve these problems, any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms. * A preliminary version of this

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Packet routing and job-shop scheduling inO(congestion+dilation) steps

Cited by 271 publications

References 4 publications

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules,

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules,

The impact of local policies on the quality of packet routing in paths, trees, and rings

Direct routing: Algorithms and complexity

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