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How often should you clean your room?

Kimball Martin 1 Krishnan Shankar 1
1 Department of Mathematics [Norman]
OU - University of Oklahoma
Abstract : 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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Kimball Martin, Krishnan Shankar. How often should you clean your room?. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.415-—444. ⟨hal-01196853⟩

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