Rotator graphs: an efficient topology for point-to-point multiprocessor networks

Corbett, Peter

doi:10.1109/71.159045

Cited by 101 publications

(50 citation statements)

References 5 publications

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“…Corbett proved that C(n) is a Hamilton sequence for the rotator graph R n [2]. Let Π C (n) = n n−1 · · · 1 • C(n) denote this Corbett Gray code of Π n .…”

Section: Hamilton Sequence For R Nmentioning

confidence: 99%

“…An explicit Hamilton cycle in R n was first constructed by Corbett [2]. Hamilton cycles were then constructed for different generalizations of R n by Ponnuswamy and Chaudhary [11] and Williams [13].…”

Section: Rotator Graphs and Hamilton Cyclesmentioning

confidence: 99%

“…Corbett introduced the term "rotator graph" when considering point-to-point multiprocessor networks, where Hamilton cycles establish indexing schemes for sorting and for mapping rings and linear arrays [2] Applications of rotator graphs include fault-tolerant file transmission by Hamada et al [5] and parallel sorting by Corbett and Scherson [3]. Properties of rotator graphs have been examined including minimum feedback sets by Kuo et al [9] and node-disjoint paths by Yasuto, Ken'Ichi, and Mario [14].…”

Section: Rotator Graphs and Hamilton Cyclesmentioning

confidence: 99%

“…to be avoided in Corbett's original application involving point-to-point multiprocessor networks [2].…”

mentioning

confidence: 99%

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Hamilton Cycles in Restricted Rotator Graphs

Stevens

Williams

2011

Lecture Notes in Computer Science

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Abstract. The rotator graph has vertices labeled by the permutations of n in one line notation, and there is an arc from u to v if a prefix of u's label can be rotated to obtain v's label. In other words, it is the directed Cayley graph whose generators are σ k := (1 2 · · · k) for 2 ≤ k ≤ n and these rotations are applied to the indices of a permutation. In a restricted rotator graph the allowable rotations are restricted from k ∈ {2, 3, . . . , n} to k ∈ G for some smaller (finite) set G ⊆ {2, 3, . . . , n}. We construct Hamilton cycles for G = {n−1, n} and G = {2, 3, n}, and provide efficient iterative algorithms for generating them. Our results start with a Hamilton cycle in the rotator graph due to Corbett (IEEE Transactions on Parallel and Distributed Systems 3 (1992) 622-626) and are constructed entirely from two sequence operations we name 'reusing' and 'recycling'.

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“…Corbett proved that C(n) is a Hamilton sequence for the rotator graph R n [2]. Let Π C (n) = n n−1 · · · 1 • C(n) denote this Corbett Gray code of Π n .…”

Section: Hamilton Sequence For R Nmentioning

confidence: 99%

Section: Rotator Graphs and Hamilton Cyclesmentioning

confidence: 99%

Section: Rotator Graphs and Hamilton Cyclesmentioning

confidence: 99%

“…to be avoided in Corbett's original application involving point-to-point multiprocessor networks [2].…”

mentioning

confidence: 99%

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Hamilton Cycles in Restricted Rotator Graphs

Stevens

Williams

2011

Lecture Notes in Computer Science

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“…nodes. Star [8], [11], bubble-sort [12], pancake [11], transposition [13], macro-star [14], rotator [15], and Faber-Moore [16] graphs have been proposed as variations of the star graph. The graphs have a smaller node degree and diameter than a hypercube with a similar number of nodes.…”

Section: Related Workmentioning

confidence: 99%

Embedding Algorithms for Bubble-Sort, Macro-star, and Transposition Graphs

Lee¹,

Sim²,

Seo

et al. 2010

Lecture Notes in Computer Science

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Abstract. Bubble-sort, macro-star, and transposition graphs are interconnection networks with the advantages of star graphs in terms of improving the network cost of a hypercube. These graphs contain a star graph as their sub-graph, and have node symmetry, maximum fault tolerance, and recursive partition properties. This study proposes embedding methods for these graphs based on graph definitions, and shows that a bubble-sort graph B n can be embedded in a transposition graph T n with dilation 1 and expansion 1. In contrast, a macro-star graph MS(2, n) can be embedded in a transposition graph with dilation n, but with an average dilation of 2 or under.

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A recurrence for the surface area of the (n,k)$$ \left(n,k\right) $$‐star graph

Gibbons,

Qiu

2024

Concurrency and Computation

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SummaryWe present a simple recurrence for the surface area of the ‐star graph, , that is, the number of nodes at a certain distance from the identity node in the graph, an important parameter for interconnection networks in parallel computing. The family of the ‐star graphs includes several popular interconnection networks such as the star graph and the alternating group network. Previously, a surface area recurrence has been obtained for a special case, for example, when , in the family of ‐star. Our recurrence gives one single recurrence for all graphs in the family, thus completely solving the surface area of ‐star for all . Compared to explicit surface area formulas previously obtained through complicated and involved combinatorial analysis and generating function approach, our derivation is more elementary and our recurrence gives a way to compute the surface area of the ‐star efficiently.

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Rotator graphs: an efficient topology for point-to-point multiprocessor networks

Cited by 101 publications

References 5 publications

Hamilton Cycles in Restricted Rotator Graphs

Hamilton Cycles in Restricted Rotator Graphs

Embedding Algorithms for Bubble-Sort, Macro-star, and Transposition Graphs

A recurrence for the surface area of the (n,k)$$ \left(n,k\right) $$‐star graph

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