A Randomized Algorithm for Cake Cutting

Cake cutting is a resource allocation problem in which a resource has to be divided fairly among a number of players. In this problem a player may not value all the parts of the resource in the same manner and different players may value the same part differently. A protocol(algorithm) to solve the cake cutting problem can learn about these valuations by asking queries to players. The goal of the protocol is to divide the resource fairly and make all the players happy by asking as few queries as possible. In 1984, Even and Paz gave an O(n logn) protocol and recently Edmonds and Pruhs proved that every deterministic protocol will ask Ω(n logn) queries. In a separate paper, they also gave an O(n) randomized approximate fair protocol with O(1) success probability. We improved their algorithm by providing O(n) randomized protocol with O(1− 1 poly(n) ) success probability.