Universal Routing Strategies for Interconnection Networks

Scheideler, Christian; Leeuwen, Jan van; Hartmanis, Juris; Goos, G.

doi:10.1007/bfb0052928

Cited by 48 publications

(73 citation statements)

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“…We recommend consulting [31], which is a very readable presentation of this problem as well as many more details and variants than we cover here. We note that [28] studied a more general version of the packet-routing problem, so their choice of parameters was not (and could not be) optimized.…”

Section: Packet Routingmentioning

confidence: 99%

“…The general strategy for our construction is based on [31] with some small changes to parameters. We will add random delays to each packet, and then allow the packet to move through each of its edges in turn without hesitation.…”

Section: 1mentioning

confidence: 99%

“…See [31] for a much more thorough explanation of this process. Now that we have reduced to constant-sized intervals, we are no longer interested in asymptotic arguments, and come down to specific numbers.…”

Section: 1mentioning

confidence: 99%

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The Moser-Tardos Framework with Partial Resampling

Harris

Srinivasan

2013

2013 IEEE 54th Annual Symposium on Foundations of Computer Science

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Abstract. The resampling algorithm of Moser & Tardos is a powerful approach to develop constructive versions of the Lovász Local Lemma (LLL). We generalize this to partial resampling: when a bad event holds, we resample an appropriately-random subset of the variables that define this event, rather than the entire set as in Moser & Tardos. This is particularly useful when the bad events are determined by sums of random variables. This leads to several improved algorithmic applications in scheduling, graph transversals, packet routing etc. For instance, we improve the approximation ratio of a generalized D-dimensional scheduling problem studied by Azar & Epstein from O(D) to O(log D/ log log D), and settle a conjecture of Szabó & Tardos on graph transversals asymptotically. As a point of comparison with the MT algorithm, we show a family of constraint satisfaction problems that does not have "locality" (every constraint is affected by every variable), and so the LLL and the Moser-Tardos algorithm do not give any useful results; however, our method gives strong scale-free approximation ratios and terminates in expected polynomial time for this family.

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Section: Packet Routingmentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

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The Moser-Tardos Framework with Partial Resampling

Harris

Srinivasan

2013

2013 IEEE 54th Annual Symposium on Foundations of Computer Science

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“…We will improve some choices of parameters, as well as examine more closely instances in which the congestion is controlled on very small scales. So, we will first examine the packet-routing problem using the standard LLL; this extends the analysis of [29] and [25]. We will then show how to enhance this to handle the nonlinear increasing functions that arise, by using our assignment LLL.…”

Section: Overviewmentioning

confidence: 99%

“…A seminal result proven in [20] (via iterated application of the LLL, which has become a key tool in its own right [21]) is that in fact T ≤ O(C + D) for all input instances, using constant-sized queues at the edges; both this result and its approach, have been used in much work in networks and combinatorial optimization. This argument was refined and simplified in [29,25], leading to a (constructive) bound of 23.4(C + D) [25]. By introducing several new ideas in scheduling packets along time intervals, we improve this to 7.26(C + D) (non-constructively) and 8.84(C + D) (constructively), thus approaching the simple lower bound for this fundamental problem.…”

Section: Introductionmentioning

confidence: 99%

Constraint satisfaction, packet routing, and the lovasz local lemma

Harris

Srinivasan

2013

Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing

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Constraint-satisfaction problems (CSPs) form a basic family of N P -hard optimization problems that includes satisfiability. Motivated by the sufficient condition for the satisfiability of SAT formulae that is offered by the Lovász Local Lemma, we seek such sufficient conditions for arbitrary CSPs. To this end, we identify a variable-covering radius-type parameter for the infeasible configurations of a given CSP, and also develop an extension of the Lovász Local Lemma in which many of the events to be avoided have probabilities arbitrarily close to one; these lead to a general sufficient condition for the satisfiability of arbitrary CSPs. One primary application is to packet-routing in the classical Leighton-Maggs-Rao setting, where we introduce several additional ideas in order to prove the existence of near-optimal schedules; further applications in combinatorial optimization are also shown.

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On the Benefit of Supporting Virtual Channels in Wormhole Routers

Cole

Maggs²,

Sitaraman³

2001

Journal of Computer and System Sciences

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This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L flits each, whose paths have congestion C and dilationÂB) flit steps, where a flit step is the time taken to transmit B flits, i.e., one flit per virtual channel, across a physical channel. We also prove a nearly matching lower bound; i.e., for any values of C, D, B, and L, where C, D B+1 and L=(1+0(1)) D, we show how to construct a network and a set of L-flit messages whose paths have congestion C and dilation D that require 0(LCD 1ÂB ÂB) flit steps to route. These upper and lower bounds imply that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor, i.e., a factor significantly larger than B. We also present a simple randomized wormhole routing algorithm for the butterfly network. The algorithm routes any q-relation on the inputs and outputs

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Universal Routing Strategies for Interconnection Networks

Cited by 48 publications

References 0 publications

The Moser-Tardos Framework with Partial Resampling

The Moser-Tardos Framework with Partial Resampling

Constraint satisfaction, packet routing, and the lovasz local lemma

On the Benefit of Supporting Virtual Channels in Wormhole Routers

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