Confidently Cutting a Cake into Approximately Fair Pieces
نویسندگان
چکیده
We give a randomized protocol for the classic cake cutting problem that guarantees approximate proportional fairness, and with high probability uses a linear number of cuts.
منابع مشابه
Cake Cutting - Fair and Square
The classic fair cake-cutting problem [Steinhaus, 1948] is extended by introducing geometric constraints on the allocated pieces. Specifically, agents may demand to get their share as a square or a rectangle with a bounded length/width ratio. This is a plausible constraint in realistic cake-cutting applications, notably in urban and agricultural economics where the “cake” is land. Geometric con...
متن کاملSome Recent Results on Pie Cutting
For cake cutting, cuts are parallel to an axis or segment and yield rectangular pieces. As such, cutting a cake is viewed as dividing a line segment. For pie cutting, cuts are radial from the center of a disc to the circumference and yield sectors or wedge-shaped pieces. As such, cutting a pie is viewed as dividing a circle. This difference in topology is apparent in the minimal number of cuts ...
متن کاملDivide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure
Properties of discrete cake-cutting procedures that use a minimal number of cuts (n – 1 if there are n players) are analyzed. None is always envy-free or efficient, but divideand-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n ≥ 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, the...
متن کاملH R C C *
Fair cake-cutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to “cut” pieces of the cake into specified ratios. Many distributed computing problems which involve resource sharing can be expressed as...
متن کاملCake-Cutting Is Not a Piece of Cake
Fair cake-cutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to “cut” pieces of the cake into specified ratios. One of the most interesting open questions is to determine the minimum number of cuts ...
متن کامل