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

TL;DR
This paper investigates a combinatorial optimization problem related to cleaning frequency, providing asymptotic analysis, bounds, and conjectures for the optimal cleanup time based on the number of objects.
Contribution
It introduces a new combinatorial problem motivated by cleaning frequency and offers asymptotic bounds, approximate solutions, and conjectures for the optimal cleanup time.
Findings
Proved a logarithmic upper bound for cleanup time
Solved an approximate version of the problem
Conjectured a precise logarithmic asymptotic
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
