The Folded Petersen Network : A New Communication-Efficient Multiprocessor Topology

Öhring, Sabine R.; Das, Sajal K.

doi:10.1109/icpp.1993.175

Cited by 12 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

Bezrukov

Das

Elsässer

2000

Annals of Combinatorics

View full text Add to dashboard Cite

show abstract

“…Our technique can also be applied to other less regular variants of the hypercube such as incomplete hypercubes [43], Fibonacci cubes [44], folded Petersen networks [45,46] and star graphs [47]. Therefore, it is also necessary to change the definition of a (k, h, o, λ)tree slightly and, as a consequence, the first embedding step (Theorem 4.2).…”

Section: Other Topologiesmentioning

confidence: 99%

Efficient Embeddings into Hypercube-like Topologies

Heun¹

2003

The Computer Journal

View full text Add to dashboard Cite

Embeddings of various graph classes into hypercubes have been widely studied. Almost all these classes are regularly structured graphs such as meshes, complete trees or pyramids. In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs. An extended edge bisector is an edge bisector with the additional property that a certain subset of the vertices is distributed more or less evenly among the two halves of the bisected graph. The dilation and congestion of our embedding depends on the quality of the extended edge bisector. Moreover, if the extended bisection can be computed efficiently on the hypercube, then so can the embedding. Our embedding technique can also be applied to embeddings into hypercube-like topologies such as folded hypercubes, twisted cubes, crossed cubes, Möbius cubes, Fibonacci cubes or star graphs.

show abstract

“…Although the Petersen graph does not contain a Hamiltonian cycle (one which contains all nodes exactly once), it is easy to show that the hyper Petersen network HP,, for n -> 4, is Hamiltonian. Furthermore, unlike the binary hypercubes, rings of odd SOUl"CC (11, ,I) ( 0 0 , 3 ) I k ( 0 0 , 5 ) (00,3) (01,5) (01,3) (10,1) (10,7) lengths can be embedded into hyper Petersen networks and this property increases its flexibility.…”

Section: Rings and Linear Arraysmentioning

confidence: 99%

“…ne of the important aspects of a messagepassing parallel computer is its interconnection network topology, which can be represented as an undirected graph such that each node represents a processor-memory module and an edge is a bidirectional communication link between two processors. Several network topologies have been proposed including trees, meshes, shuffle-exchange [1], hypercubes, cube connected cycles [2], pyramids [3], recursive networks [4], stars and pancakes [5], de Bruijn networks [6], folded Petersen networks [7] and so on.…”

Section: Introductionmentioning

confidence: 99%

Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

1995

Self Cite

View full text Add to dashboard Cite

A new hypercube-like topology, called the hyper Petersen (HP) network, is proposed and analyzed, which is constructed from the well-known cartesian product of the binary hypercube and the Petersen graph of ten nodes.This topology is an attractive candidate for multiprocessor interconnection having such desirable properties as regularity, high symmetry and connectivity, and logarithmic diameter. For example, an n-dimensional hyper Petersen network, HPn, with N=1.25 * 2n nodes is a regular graph of degree and node-connectivity n and diameter n–1 , whereas an (n–1)-dimensional binary hypercube, Qn−1 , with the same diameter covers only 2n−1 nodes, each of degree (n–1). Thus the HP topology accommodates 2.5 times extra nodes than Qn−1 at the cost of increasing the node-degree by one. With the same degree and connectivity of n, the diameter of the HPn network is one less than that of Qn, yet having 1.25 times larger number of nodes.Efficient routing and broadcasting schemes are presented, and node-disjoint paths in HPn, are computed even under faulty conditions. The versatility of the hyper Petersen networks is emphasized by embedding rings, meshes, hypercubes and several tree-related topologies into it. Contrary to the hypercubes, rings of odd lengths, and a complete binary tree of height n–1 permit subgraph embeddings in HPn.

show abstract

The Folded Petersen Network : A New Communication-Efficient Multiprocessor Topology

Cited by 12 publications

References 7 publications

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

Efficient Embeddings into Hypercube-like Topologies

Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

Contact Info

Product

Resources

About