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## Hamilton Cycles in Restricted Rotator Graphs

Citations: | 1 - 1 self |

### Citations

38 |
Loopless algorithms for generating permutations, combinations, and other combinatorial configurations
- Ehrlich
- 1973
(Show Context)
Citation Context ... ‘recycling’. We also provide an algorithm for constructing the Hamilton sequences. The algorithm is loopless since successive values in the sequence are obtained in worst-case O(1)-time (see Ehrlich =-=[4]-=- for the first use of this term). Section 2 formally defines the ‘reuse’ and ‘recycle’ operations. Section 3 constructs the three Hamilton cycles and proves that two of the constructions are correct. ... |

16 |
The Art of Computer Programming, Volume 4, Generating All Tuples and Permutations, Fascicle 2
- Knuth
- 2005
(Show Context)
Citation Context ...≤ i ≤ n. Loopless Algorithm H in The Art of Computer Programming generates multi-radix numbers in reflected Gray code order, meaning that successive strings differ by ±1 in a single symbol (see Knuth =-=[8]-=- pg. 20). In the special case of staircase strings, Algorithm H generates the ± indices according to the staircase sequence. For example, the Gray code appears below for n = 3 111, 112, 113, 123, 122,... |

10 |
Sorting in Mesh Connected Multiprocessors
- Corbett, Scherson
- 1992
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Citation Context ...chemes 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]. Other variations of rotator graphs inclu... |

9 |
Doubly adjacent Gray codes for the symmetric group. Linear and Multilinear Algebra,
- Compton, Williamson
- 1993
(Show Context)
Citation Context ... Cayley graph, where undirected Cayley graphs include the inverse of each generator. In particular, a Hamilton cycle was constructed for Cay({σ2, σn}, Sn) by Compton and Williamson in a 50-page paper =-=[1]-=-. 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 arr... |

8 | Loopless Generation of Multiset Permutations Using a Constant Number of Variables by Prefix Shifts
- Williams
- 2009
(Show Context)
Citation Context ...d lists. An explicit Hamilton cycle in Rn was first constructed by Corbett [2]. Hamilton cycles were then constructed for different generalizations of Rn by Ponnuswamy and Chaudhary [11] and Williams =-=[13]-=-. Hamilton cycle constructions for Rn({n − 1, n}) were proposed as an open problem by Knuth, and this was answered by Ruskey and Williams [12]. Observe that σn must be included in a restricted rotator... |

7 |
An Explicit Universal Cycle for the (n−1)- Permutations of an n-set
- Ruskey, Williams
- 2010
(Show Context)
Citation Context ...tions of Rn by Ponnuswamy and Chaudhary [11] and Williams [13]. Hamilton cycle constructions for Rn({n − 1, n}) were proposed as an open problem by Knuth, and this was answered by Ruskey and Williams =-=[12]-=-. Observe that σn must be included in a restricted rotator graph in order to generate the entire symmetric group Sn. Moreover, σn and σc are not sufficient for generating Sn when c is an arbitrary fix... |

3 | Faster Generation of Shorthand Universal Cycles for Permutations
- Holroyd, Ruskey, et al.
(Show Context)
Citation Context ...re the labels can have repeated symbols [13]. The relationship between Hamilton cycles of Rn(n − 1, n) and universal cycles of Πn is discussed by Holroyd, Ruskey, and Williams along with applications =-=[6, 7]-=-.1.2 New Results We construct a new Hamilton cycle in Rn({n−1, n}) and the first Hamilton cycle in Rn({2, 3, n}). The new constructions are intimately related to Corbett’s original Hamilton cycle in ... |

2 |
Yoshihide Igarashi, Nonadaptive Fault-Tolerant File Transmission
- Hamada, Bao, et al.
- 1996
(Show Context)
Citation Context ...works, 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 Mar... |

2 |
Kung-Kuei Lin An Efficient Algorithm for Minimum Feedback Vertex
- Kuo, Hsu, et al.
- 2009
(Show Context)
Citation Context ...ude 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]. Other variations of rotator graphs include incomplete rotator graphs [11], the bi-rotator graph (see Lin and Hsu [10]), and graphs where t... |

2 |
Topological Properties of Bi-Rotator Graphs
- Lin, Hsu
(Show Context)
Citation Context ...ack sets by Kuo et al [9] and node-disjoint paths by Yasuto, Ken’Ichi, and Mario [14]. Other variations of rotator graphs include incomplete rotator graphs [11], the bi-rotator graph (see Lin and Hsu =-=[10]-=-), and graphs where the labels can have repeated symbols [13]. The relationship between Hamilton cycles of Rn(n − 1, n) and universal cycles of Πn is discussed by Holroyd, Ruskey, and Williams along w... |

2 |
Embedding of Cycles in Rotator and Incomplete Rotator Graphs
- Ponnuswamy, Chaudhary
- 1994
(Show Context)
Citation Context ...operties are called lists. An explicit Hamilton cycle in Rn was first constructed by Corbett [2]. Hamilton cycles were then constructed for different generalizations of Rn by Ponnuswamy and Chaudhary =-=[11]-=- and Williams [13]. Hamilton cycle constructions for Rn({n − 1, n}) were proposed as an open problem by Knuth, and this was answered by Ruskey and Williams [12]. Observe that σn must be included in a ... |

1 |
Shorthand Universal Cycles for Permutations, Algorithmica
- Holroyd, Ruskey, et al.
(Show Context)
Citation Context ...re the labels can have repeated symbols [13]. The relationship between Hamilton cycles of Rn(n − 1, n) and universal cycles of Πn is discussed by Holroyd, Ruskey, and Williams along with applications =-=[6, 7]-=-.1.2 New Results We construct a new Hamilton cycle in Rn({n−1, n}) and the first Hamilton cycle in Rn({2, 3, n}). The new constructions are intimately related to Corbett’s original Hamilton cycle in ... |