How often should you clean your room?

Kimball Martin; Krishnan Shankar

How often should you clean your room?

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arxiv 1305.1984 v2 pith:RHZYTW74 submitted 2013-05-09 math.CO math.PR

Kimball Martin , Krishnan Shankar This is my paper · ORCID

classification math.COmath.PR

keywords roomyourcleanlogarithmicobjectsoftenproblemapproximate

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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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