Universal schemes for parallel communication

Valiant, Leslie G.; Brebner, Gordon

doi:10.1145/800076.802479

Cited by 513 publications

(257 citation statements)

References 13 publications

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“…The oblivious routing problem has been investigated before (e.g., Azar et al 2003;Bienkowski et al 2003;Borodin and Hopcroft 1985;Gupta et al 2006;Räcke 2002;Valiant and Brebner 1981). Most of the above mentioned works dwell upon algorithmic approaches, while Applegate and Cohen (2003) and Belotti and Pınar (2008) resort to mathematical programming models.…”

Section: Oblivious Routing Under Polyhedral Demand Uncertaintymentioning

confidence: 99%

OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty

2009

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We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and a routing is sought with a fair performance for any feasible traffic matrix in the polyhedron. The problem accurately reflects real world networks, where demands can only be estimated, and models one of the main traffic forwarding technologies, Open Shortest Path First (OSPF) routing with equal load sharing. This is an NP-hard problem as it generalizes the problem with a fixed demand matrix, which is also NP-hard.We prove that the optimal oblivious routing under polyhedral traffic uncertainty on a non-OSPF network can be obtained in polynomial time through Linear Programming. Then we consider the OSPF routing with equal load sharing under polyhedral traffic uncertainty, and present a compact mixed-integer linear programming formulation with flow variables. We propose an alternative formulation and a branchand-price algorithm. Finally, we report and discuss test results for several network instances.

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Section: Oblivious Routing Under Polyhedral Demand Uncertaintymentioning

confidence: 99%

OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty

2009

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“…We first convert an input instance of the permutation to a path-routing problem using Valiant's method [28,29]: we use two butterflies connected back to back, and each packet uses a path to an intermediate random node in the output of the first butterfly. The path selection guarantees that the congestion is O(lg n), with high probability.…”

Section: Meshmentioning

confidence: 99%

“…We study permutation routing problems on the butterfly, in which each input node is the source of one packet, and each output node is the destination of one packet. In order to solve the permutation problems efficiently, we will use Valiant's scheme [28,29] which uses two back to back butterflies where packets choose random intermediate nodes before reaching their destinations. Thus, we first study the random destination problem on a butterfly, which we then use to solve permutation routing problems.…”

Section: Butterflymentioning

confidence: 99%

“…some edges are hot-spots (see [23,Section 4.2]). In order to avoid hot-spots, Valiant [28,29] proposed the following alternative scheme to route permutation routing problems in a butterfly-like network. Take two butterflies and connect them back to back, so that the outputs of the first butterfly are connected to the respective outputs of the the second butterfly.…”

Section: Permutations On Butterflymentioning

confidence: 99%

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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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“…Permutation routing on mesh-connected computers has been extensively investigated [9,10,12,13,14,16,17,22,25,29]. In permutation routing, each processor initially has a packet to send, and packets have unique destinations.…”

Section: Introductionmentioning

confidence: 99%

Routing with Locality on Meshes with Buses

Cheung

Lau

1996

Journal of Parallel and Distributed Computing

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packets is bounded by d, the authors have presented in [6] a d ϩ O(d/f (d)) step, O( f (d)) buffer size routing algorithm which is asymptotically optimal if f (d) is chosen to be a large constant. In our study, we assume all the processors operate in synchronous MIMD mode. At any time step, each processor can communicate with all of its grid neighbors and can both send and receive one packet along each mesh link. In addition, processors can also store packets in their own queues. This model (hereafter referred to as the base model) is the same as the ones used in [9, 10, 12-16, 22, 25].The main disadvantage of the mesh topology is its large diameter, which has direct impact on the communication times of many parallel algorithms. Augmenting arrays of processors with various faster mechanisms has been suggested as a means to speed up communication among the processors. Examples are meshes with multiple buses which have a bus in each column and each row [1,20], generalized meshes with multiple buses which are composed of smaller meshes with multiple buses [8], meshes with separable row and column buses in which row/column buses can be separated into multiple shorter buses through turning on/off bus switches [24], and reconfigurable meshes in which links can be connected to form buses [2]. These enhanced meshes are capable of solving problems that only require a limited amount of global communication significantly faster. This paper shows how to utilize these buses in some ''high-bandwidth'' routing problems.In all the related bused mesh models, except reconfigurable meshes, broadcast buses are added to the base model. Each broadcast bus is connected to a set of processors. In each time step, only one processor attached to a bus can send a packet via the bus. In addition, a processor can receive packets from all the buses attached to it in a time step. A number of proposed bused mesh models assume the propagation delay of a bus to be a constant which is independent of the number of processors attached to it. This assumption is thought to be a reasonable one in practical situations [1,2,3,20,27]. However, Lu et al. [18] investigated physical implementations of buses and found that short buses and long buses do have a difference in performance and that the constant-delay assumption is more appropriate with short-bus models. In this paper, we assume the propagation delay of the buses to be one time step which is also assumed in [1,8,17,27]. As we will see, JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 33, 84-90 (1996) Routing with locality is studied for meshes with buses. In this problem, packets' distances are bounded by a value, d, which is less than the diameter of the network. This problem arises naturally when specific known algorithms are implemented on meshes. Solving this problem in ordinary meshes requires at least a routing time of d steps. To do better than this, we propose adding a kind of short bus to ordinary meshes. By using a technique which we call iterative walk-and-ride, we show how the routing ...

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Universal schemes for parallel communication

Cited by 513 publications

References 13 publications

OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty

OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty

Direct routing: Algorithms and complexity

Routing with Locality on Meshes with Buses

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