Reducing communication costs for sorting on mesh-connected and linearly connected parallel computers

Park, Arvin; Balasubramanian, K.

doi:10.1016/0743-7315(90)90083-2

Cited by 13 publications

(3 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later, Kunde [lo] matched this time bound with a deterministic algorithm and a queue length of 2. Park and Balasubramanian [18] proved that 2 -2 sorting can be performed on an n x n Mesh in an optimal 3 n + o ( n ) steps. Subsequently Kunde [lo] gave an algorithm for kk sorting that runs in [k/41,2n + k n / 2 + o ( k n ) time with a queue length of k, for any k > 4.…”

Section: Known and New Resultsmentioning

confidence: 99%

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

Section: Known and New Resultsmentioning

confidence: 99%

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

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%

“…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%