Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Thursday, November 21, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Anders Martinsson


Mastermind is a classical board game in which Codemaker creates a hidden codeword consisting of a sequence of length n where each element can be one of k colors. Codebreaker must then figure out the hidden codeword by making as few queries as possible. For the commercial version, n=4 and k=6, it was shown by Knuth (1977) that Codebreaker can always win in 5 moves. The general version has gained some attention in part due to its connection to the boardgame, and in part due to its connection to classical problems in information theory. In 1983, Chvátal showed surprisingly that a simple random strategy is optimal for Codebreaker whenever k\leq n^{1-\eps}. For larger k, in particular k=n, his approach leaves a gap of \Omega(n) and O(n \log n) for the minimum number of queries. In 2016, it was shown by Doerr, Doerr, Spöhel, Thomas how codebreaker can win in O(n \log \log n) steps. In this talk, I will present recent work showing that the minimum number of queries needed for n=k Mastermind is in fact \Theta(n). This is joint work with Pascal Su.

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