Discrete Mathematics & Theoretical Computer Science, Vol 17, No 1 (2015)

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How often should you clean your room?

Kimball Martin, Krishnan Shankar


We introduce and study a combinatorial optimization problem motivated by the question in the title. In the simple case where you use all objects in your room equally often, we investigate asymptotics of the optimal time to clean up in terms of the number of objects in your room. In particular, we prove a logarithmic upper bound, solve an approximate version of this problem, and conjecture a precise logarithmic asymptotic.

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