Journal of the ACM (JACM)
Rotator Graphs: An Efficient Topology for Point-to-Point Multiprocessor Networks
IEEE Transactions on Parallel and Distributed Systems
Sorting in Mesh Connected Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming)
Loopless generation of multiset permutations using a constant number of variables by prefix shifts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An efficient algorithm for minimum feedback vertex sets in rotator graphs
Information Processing Letters
An explicit universal cycle for the (n-1)-permutations of an n-set
ACM Transactions on Algorithms (TALG)
Faster generation of shorthand universal cycles for permutations
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Embedding of cycles in rotator and incomplete rotator graphs
SPDP '94 Proceedings of the 1994 6th IEEE Symposium on Parallel and Distributed Processing
Shorthand Universal Cycles for Permutations
Algorithmica - Special Issue: Computing and Combinatorics
The greedy gray code algorithm
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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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 $\sigma_{k} := (1 \ 2 \ \cdots \ k)$ 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'.