Folded Petersen cube networks: new competitors for the hypercubes

Öhring, Sabine R.; Das, Sajal K.

doi:10.1109/71.485505

Cited by 61 publications

(16 citation statements)

References 21 publications

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“…Consider the edge-isoperimetric problem on the product graph P n m P n o Q m . These families of graphs are called folded Petersen cubes [16,17] and are extensively studied to model multiprocessor interconnection networks. It is an easy exercise to ensure oneself that the order È n m satisfies the consistency property [8] similar to Lemma 2.1.…”

Section: Products Of Petersen Powers With Hypercubesmentioning

confidence: 99%

“…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%

“…We extend these results to the product graph P n m P n o Q m , where Q m is the m-dimensional hypercube. The graphs P n m , called the folded Petersen cubes, were first studied byÖhring and Das [16,17]. It is interesting that, in this case, a lexicographic-type order is optimal.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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: Products Of Petersen Powers With Hypercubesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

Bezrukov

Das

Elsässer

2000

Annals of Combinatorics

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“…Other comparative attributes of the HO are detailed in Tables I and II. Similarly, a variety of other interconnects and emulation approaches exist in literature [11,24,30,31,36] among others However, most current works in parallel algorithms chiefly emphasize the algorithm's stages for data computations on a speci:fic embedding. The communication patterns required for initial data placement on nodes, and also for positioning the data over each phase of an algorithm's operation are still the more expensive operations which receive lesser consideration.…”

Section: Introductionmentioning

confidence: 99%

Design of a Parallel Interconnect Based on Communication Pattern Considerations

Suri

Mendelson

2001

Parallel Algorithms and Applications

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An interconnect's versatility is usually described by its ability to support a variety of algorithmic patterns based on the physical or logical embeddings within its topology that match the desired algorithmic patterns. However, most such embeddings are available on a discrete basis, though a particular algorithm may require a variety of embeddings during different phases of its operation. To provide for such varying embedded topology needs, we propose a simple and VLSI realizable interconnect structure, termed as a Union Graph (UG), which combines two discrete interconnects, with very individual and distinctive capabilities, through a union operation. We present the union of the binary deBruijn graph (BDG) and a Torus to demonstrate the effectiveness of this approach. The focus is on providing practical usability of the network for algorithmic support rather than on graph properties. We highlight the importance of communication aspects of different execution phases in designing an algorithmically specialized interconnect. A set of examples are used to demonstrate the UG's versatility for algorithmic support.

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“…However, many Cayley graphs have a vertex degree that increases with the number of vertices in the graph logarithmically or sublogarithmically. They include the Hypercubes [5], Star graphs and Pancake graphs [11], and the folded Peterson cube networks [9]. For network construction, we may only be able to support a fixed number of I/O ports at each vertex, and hence a constant degree network, e.g., the Cube-Connected Cycles [10], the ShuffleExchange Permutation Network [8], the Rotation-Exchange Network [15], and the interconnection networks of fixed degree four [12,14].…”

Section: Introductionmentioning

confidence: 99%