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Pancake problems with restricted prefix reversals and some corresponding Cayley networks

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2 Author(s)
D. W. Bass ; Comput. Sci. Program, Texas Univ., Dallas, TX, USA ; I. H. Sudborough

The pancake problem concerns the number of prefix reversals (“flips”) needed to sort the elements of an arbitrary permutation, which is the diameter of the n-dimensional pancake network. We restrict the problem by allowing only a few of the possible n-1 flips. Let fi denote a flip of size i. We consider sets with either O(1) flips or log2 n flips, and explore their corresponding Cayley networks, such as: The Subcuben network, for n=2k, defined by the log2 n flips {f2 ,f4,f8...fn}. Subcuben is isomorphic to a network obtained from an (n-1) dimensional hypercube, Qn-1, by deleting all but log2 n of the edges incident to each of its nodes, has diameter (3n/2)-2 (we give an optimum routing algorithm), and hosts Qn-1 with nearly optimum dilation. The Triadn network where n is odd and [n/2] mod 4≠0, defined by the set of flips {f[n/2] f[n/2] fn}. Triad n has n! nodes and diameter Θ(n log2 n). Both the n-dimensional shuffle-exchange and shuffle-exchange permutation networks can be emulated by Triadn with constant slowdown

Published in:

Parallel Processing, 1998. Proceedings. 1998 International Conference on

Date of Conference:

10-14 Aug 1998