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

Date and Time: Thursday, June 16, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Jerri Nummenpalo

Constant time algorithm for middle levels Gray codes

For any n > 0 a middle levels Gray code is a cyclic listing of all n-element and (n+1)-element subsets of {1,2,...,2n+1} such that any two consecutive subsets differ by adding or removing a single element. The existence of a middle levels Gray code for every n > 0 was long conjectured by the Middle levels conjecture and it was recently settled on the positive by Mütze. In this talk we address the question of efficiently generating a Gray code: Given a subset S and an integer i, how to generate the next i elements following S in a middle levels Gray code fast? Our result is an algorithm with optimal time and space requirements. Each new set is generated in time O(1) on average and the required space is O(n). Our proof can also be viewed as a simplified and more combinatorial proof of the Middle levels theorem. This is joint work with Torsten Mütze.

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