Paper Info
Title
The Complexity of Cake Cutting with Unequal Shares
Abstract
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.
Year
DOI
Venue
2020
10.1145/3380742
ACM Transactions on Algorithms
Keywords
DocType
Volume
Cake cutting,fair division,proportional division,unequal shares
Journal
16
Issue
ISSN
Citations 
3
1549-6325
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Ágnes Cseh1205.80
Tamás Fleiner224127.45