When valuations may be mixed, a moving-knife protocol can be used to find a connected proportional division using O(n^2) queries. Can this…

When valuations may be mixed, a moving-knife protocol can be used to find a connected proportional division using O(n^2) queries. Can this be improved to O(n\log n) ?

Open the “Fair division of a partly burnt cake” section on Wikipedia →

Source: List of unsolved problems in fair division (CC BY-SA 4.0)