English

How often should you clean your room?

Combinatorics 2015-09-02 v2 Probability

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.

Cite

@article{arxiv.1305.1984,
  title  = {How often should you clean your room?},
  author = {Kimball Martin and Krishnan Shankar},
  journal= {arXiv preprint arXiv:1305.1984},
  year   = {2015}
}

Comments

28 pages, minor changes, now in color with 2 graphs

R2 v1 2026-06-22T00:13:48.598Z