Martin, Kimball and Shankar, Krishnan - How often should you clean your room?

dmtcs:2109 - Discrete Mathematics & Theoretical Computer Science, June 29, 2015, Vol. 17 no. 1 (in progress)
How often should you clean your room?

Authors: Martin, Kimball and Shankar, Krishnan

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.


Source : oai:HAL:hal-01196853v1
Volume: Vol. 17 no. 1 (in progress)
Section: Analysis of Algorithms
Published on: June 29, 2015
Submitted on: January 10, 2015
Keywords: search with cleanup,combinatorial optimization,coupon collector’s problem,sequential occupancy,Stirling numbers of the second kind,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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