Efficient communication in the folded Petersen interconnection networks

Öhring, Sabine R.; Das, Sajal K.

doi:10.1007/3-540-58184-7_87

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…Note that P is a vertex-symmetric as well as an edge-symmetric graph. The graphs P n , known as folded Petersen networks, were proposed and extensively studied byÖhring and Das [9,[13][14][15][16] as a communication-efficient interconnection network topology for multiprocessors. By definition, P n is also regular, vertex-and edge-symmetric with 10 n vertices, degree 3n and diameter 2n.…”

Section: Introductionmentioning

confidence: 99%

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

Bezrukov

Das

Elsässer

2000

Annals of Combinatorics

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In this paper we introduce a new order on the set of n-dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph P n , defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of P n are also derived. These results are then generalized for the cartesian product of P n and the m-dimensional binary hypercube. Problem 1.2. Find a subset of vertices of a given graph, such that the number of edges in the subgraph induced by this subset is maximal among all induced subgraphs with the same number of vertices.

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Section: Introductionmentioning

confidence: 99%

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

Bezrukov

Das

Elsässer

2000

Annals of Combinatorics

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“…As far as we can tell, this algorithm was rst reported (in Japanese) by Take ( 40]) for the hypercube network topology. Later, several variations of this algorithm were developed (still dependent upon network topology) such as the Optimal Circuit Switched, Hypercube, or Mesh Algorithm ( 37,10,25,36,12,13,14,1,31,23,33,19,24]), the Pairwise-Exchange (PEX) algorithm ( 43,41,42]), and the general Linear Permutation algorithm ( 45]). For our comparison, we consider the standard algorithm consisting of p steps, such that during step i, (0 i p 1), processor j sends data labelled for processor k = i j directly to P k .…”

Section: Comparison With Single-phase Algorithmsmentioning

confidence: 99%

“…24,39,14,25], or other circuit switched network machines, e.g. 33,19,31,37]) tend to be network or machine dependent, and thus not e cient when ported to current parallel machines. In this paper, we introduce a novel deterministic algorithm that is shown to be both e cient and scalable across a number of di erent platforms.…”

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confidence: 99%

Practical parallel algorithms for personalized communication and integer sorting

Bader¹,

Helman²,

JáJá³

1996

ACM J. Exp. Algorithmics

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A fundamental challenge for parallel computing is to obtain high-level, architecture independent, algorithms which efficiently execute on general-purpose parallel machines. With the emergence of message passing standards such as MPI, it has become easier to design efficient and portable parallel algorithms by making use of these communication primitives. While existing primitives allow an assortment of collective communication routines, they do not handle an important communication event when most or all processors have non-uniformly sized personalized messages to exchange with each other. We focus in this paper on the h-relation personalized communication whose efficient implementation will allow high performance implementations of a large class of algorithms. While most previous h-relation algorithms use randomization, this paper presents a new deterministic approach for h-relation personalized communication with asymptotically optimal complexity for h>p 2 . As an application, we present an efficient algorithm for stable integer sorting. The algorithms presented in this paper have been coded in Split-C and run on a variety of platforms, including the Thinking Machines CM-5, IBM SP-1 and SP-2, Cray Research T3D, Meiko Scientific CS-2, and the Intel Paragon. Our experimental results are consistent with the theoretical analysis and illustrate the scalability and efficiency of our algorithms across different platforms. In fact, they seem to outperform all similar algorithms known to the authors on these platforms.

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“…The applications include the wirelength problem, the bisection width and the edge congestion problem of graph embedding, modeling the brain, the cutwidth problem and graph partitioning. The graphs in Theorem 1.7 are called folded Petersen networks and have been studied in [20,22,21,18,13] as a communication-efficient interconnection network topology for multiprocessors. The graphs in Theorem 1.8 are called folded Petersen cubes and have been studied in [13,19].…”

Section: Introductionmentioning

confidence: 99%