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

dmtcs:2109 - Discrete Mathematics & Theoretical Computer Science, June 29, 2015, Vol. 17 no. 1 - https://doi.org/10.46298/dmtcs.2109
How often should you clean your room?Article

Authors: Kimball Martin 1; Krishnan Shankar 1

  • 1 Department of Mathematics [Norman]

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.


Volume: Vol. 17 no. 1
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]
Funding:
    Source : OpenAIRE Graph
  • Rigidity theorems in geometry and topology; Funder: National Science Foundation; Code: 1104352

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