How to keep floors clean with multiple dogs without spending hours

What people tried

Every workaround mentioned in the threads below. We haven’t tested any of them — and nobody here is claiming they worked.

1. 1
   Washing the floors twice a day
2. 2
   Using a robot vacuum cleaner
3. 3
   Mopping with unscented castille soap and hot water instead of residue-leaving cleaners
4. 4
   Using air purifiers and dehumidifiers
5. 5
   Running box fans with HVAC filters
6. 6
   Switching to non-clay cat litter to reduce tracking and smell
7. 7
   Restricting cat access to certain parts of the house using French doors

In their words

Unedited, grouped by where they were said, most upvoted first within each place, each linked to the thread it came from.