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Pancake Problems with Restricted Prefix Reversals and some Corresponding Cayley Networks (1998)
| Citations: | 2 - 2 self |
BibTeX
@MISC{Bass98pancakeproblems,
author = {Douglas W. Bass and I. Hal Sudborough},
title = {Pancake Problems with Restricted Prefix Reversals and some Corresponding Cayley Networks},
year = {1998}
}
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Abstract
The pancake problem, which has attracted considerable attention [10, 12, 9, 15], concerns the number of prefix reversals or flips needed to sort the elements of an arbitrary permutation. The number of prefix reversals to sort permutations is also the diameter of the often studied n-dimensional Pancake network P n [3, 4, 5, 8, 14, 16]. We consider restricted pancake problems, for example when only 3 of the possible n - 1 flips are allowed. Let f i denote a flip of size i. Each flip is itself a permutation. For example, a flip of size 4, i. e., f 4 , on eight symbols has the effect of changing, say, 3 5 1 2 4 6 8 7 into 2 1 5 3 4 6 8 7. f 4 is the permutation 4 3 2 1 5 6 7 8. We investigate sets of permutations corresponding to flips as generators of the symmetric group S n . Let n be the number of symbols in a permutation. We consider sets with either a constant number of generators (i. e., flips) or with log 2 n generators. In special interesting cases, the corresponding Cayley net...
