When all valuations are positive, or all valuations are negative, the Even-Paz protocol finds a connected proportional division using…

When all valuations are positive, or all valuations are negative, the Even-Paz protocol finds a connected proportional division using O(n\log n) queries, and this is optimal.

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)