On sorting by prefix reversals and the diameter of pancake networks
We show that the conjectured hardest stack of burnt pancakes, −I(n), can be sorted in 3(n+1)/2 steps, for all n≡3(mod 4) with n ≥ 23. If-I(n) is indeed hardest, then both the ”burnt” and ”unburnt” pancake networks of dimension n have diameter at most 3(n+1)/2. We also describe a 9/8 n+2 step sorting sequence for Gates and Papadimitriou's unburnt stack of pancakes, χ n , thus disproving their conjecture that 19/16n steps are required.
KeywordsPermutation Group Cayley Graph Computer Search Signed Permutation Upward Sequence
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