The complexity of cake cutting with unequal shares

An unceasing problem of our prevailing society is the fair division of goods. The problem of fair cake cutting is dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional share. In this paper, we investigate the problem of proportional division with unequal shares, where each player is entitled to receive a predetermined portion of the cake. Our contribution is twofold. First we present a protocol that delivers a proportional solution in less queries than all known algorithms. We then show that our protocol is the fastest possible by giving an asymptotically matching lower bound. Both results remain valid in a highly general cake cutting model, which can be of independent interest.