Concentrated regular data streams on grids: sorting and routing near to the bisection bound

Kunde, Manfred

doi:10.1109/sfcs.1991.185363

Cited by 37 publications

(24 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerous papers have been written on routing and sorting on the conventional mesh (see e.g., [30,28,11,14,12,25,26,24,22,7]). An excellent reference for algorithms on the conventional mesh is Leighton [13].…”

Section: Previous and New Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Mesh connected computers with fixed and reconfigurable buses: Packet routing, sorting, and selection

Rajasekaran

1993

Algorithms—ESA '93

View full text Add to dashboard Cite

Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing and sorting on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k − k routing and k − k sorting on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1 − 1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1 − 1 routing, k − k routing, and k − k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed * This research was supported in part by an NSF Research Initiation Award CCR-92-09260. Preliminary versions of some of the results in this paper were presented in the First Annual European Symposium on Algorithms, 1993. 1 in logarithmic time on a mesh with fixed buses. Most of our algorithms have considerably better time bounds than known algorithms for the same problems.

show abstract

Section: Previous and New Resultsmentioning

confidence: 99%

“…A similar indexing was used in [11] also. Figure 1 gives an example of a 6 × 6 mesh with 2 keys per node.…”

Section: Definition Of Problemsmentioning

confidence: 99%

Mesh connected computers with fixed and reconfigurable buses: Packet routing, sorting, and selection

Rajasekaran

1993

Algorithms—ESA '93

View full text Add to dashboard Cite

show abstract

“…Various algorithms have been developed for mesh-connected computers and their variants, such as tori and n-ary d-cubes, based on the assumption that a fault-free mesh (or torus, n-ary d-cube) is available [3,10,11,13,16,15,17]. Since fault tolerance is very important to parallel processing, a variety of techniques for adaptive fault-tolerant routing or reconfiguring faulty arrays have also been proposed [5,6,12,18,19,23].…”

Section: Basic Components Of Railmentioning

confidence: 99%

“…For example, it can be shown that, using techniques similar to those used in [9], an N-node 2-D array with o(N) random faults or a p-faulty array with faulty rate p = o (1) A wide variety of algorithms, such as reduction (e.g., semigroup computation), prefix computation [15], FFT [11], sorting (e.g. the algorithms proposed in [10]), and matrix multiplication, have S = O(n), and thus can run with a slowdown factor of 1+o (1) …”

Section: The Compaction/expansion Technique (Cet)mentioning

confidence: 99%

“…The scalability, compact layout, constant/small node-degree, desirable algorithmic properties, and many other advantages have made meshes, tori, and n-ary d-cubes the most popular topologies for the interconnection of parallel processors. A very large variety of algorithms have been proposed for these networks [3,10,11,13,16,15,17]. These algorithms usually assume that a faultfree mesh or torus is available, and most of them cannot be applied to faulty meshes or tori directly, even in the presence of only a small number of faulty elements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ART: robustness of meshes and tori for parallel and distributed computation

Yeh

Parhami

Proceedings International Conference on Parallel Processing

View full text Add to dashboard Cite

show abstract

k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh

Rajasekaran

1995

Journal of Algorithms

View full text Add to dashboard Cite

In this paper we present randomized algorithms for k-k routing, k-k sorting, and cut through routing. The stated resource bounds hold with high probability. The algorithm for k-k routing runs in [k/2]n+o(kn) steps. We also show that k-k sorting can be accomplished within [k/2] n+n+o(kn) steps, and cut through routing can be done in [3/4]kn+[3/2]n+o(kn) steps. The best known time bounds (prior to this paper) for all these three problems were kn+o(kn). [kn/2] is a known lower bound for all the three problems (which is the bisection bound), and hence our algorithms are very nearly optimal. All the above mentioned algorithms have optimal queue length, namely k+o(k). These algorithms also extend to higher dimensional meshes.

show abstract

Concentrated regular data streams on grids: sorting and routing near to the bisection bound

Cited by 37 publications

References 14 publications

Mesh connected computers with fixed and reconfigurable buses: Packet routing, sorting, and selection

Mesh connected computers with fixed and reconfigurable buses: Packet routing, sorting, and selection

ART: robustness of meshes and tori for parallel and distributed computation

k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh

Contact Info

Product

Resources

About