TY - JOUR A1 - Cseh, Ágnes A1 - Fleiner, Tamas T1 - The complexity of cake cutting with unequal shares JF - ACM transactions on algorithms : TALG N2 - An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on 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 article, we investigate the problem of proportional division with unequal shares, where each player is entitled to receive a predetermined portion of the cake. Our main contribution is threefold. First we present a protocol for integer demands, which delivers a proportional solution in fewer queries than all known protocols. By giving a matching lower bound, we then show that our protocol is asymptotically the fastest possible. Finally, we turn to irrational demands and solve the proportional cake cutting problem by reducing it to the same problem with integer demands only. All results remain valid in a highly general cake cutting model, which can be of independent interest. KW - Cake cutting KW - fair division KW - unequal shares KW - proportional division Y1 - 2020 U6 - https://doi.org/10.1145/3380742 SN - 1549-6325 SN - 1549-6333 VL - 16 IS - 3 PB - Association for Computing Machinery CY - New York ER -