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On sorting by prefix reversals and the diameter of pancake networks

  • Mohammad H. Heydari
  • I. Hal Sudborough
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 678)

Abstract

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.

Keywords

Permutation Group Cayley Graph Computer Search Signed Permutation Upward Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Mohammad H. Heydari
    • 1
  • I. Hal Sudborough
    • 1
  1. 1.Department of Computer ScienceThe University of Texas at DallasRichardsonUSA

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