# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, January 18, 2005, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Dejan Dukaric

## The Pancake Problem

For a permutation *R* of the integers from *1* to *n*, let *f(R)* be the smallest number of prefix reversals that will transform *R* to the identity permutation, and let *f(n)* be the largest such *f(R)* for all *R* in the symmetric group *S*_{n}, where a prefix reversal will transform one permutation to another by taking a prefix of the permutation and then reverse this prefix (example: 34251 -> 24351). In my talk I will present proofs for the upper and lower bound of *f(n)*.
An application of the pancake problem is the pancake network which looks promising as a network for parallel algorithms.

Source for the proofs:
W. Gates and C. Papadimitriou (1979), "Bounds for Sorting by Prefix Reversal"

Sources for further results:
D.S. Cohen, M. Blum (1993), "On the Problem of Sorting Burnt Pancakes"
M.H. Heydari, I.H. Sudborough (1997), "On the Diameter of the Pancake Network"

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