Approximating fair division with a limited number of cuts
Journal of Combinatorial Theory Series A
An Approximation Scheme for Cake Division with a Linear Number of Cuts
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Cake cutting really is not a piece of cake
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Confidently Cutting a Cake into Approximately Fair Pieces
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Negotiation criteria for multiagent resource allocation
The Knowledge Engineering Review
Degrees of Guaranteed Envy-Freeness in Finite Bounded Cake-Cutting Protocols
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Meta-envy-free cake-cutting protocols
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
The efficiency of fair division with connected pieces
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Cake cutting really is not a piece of cake
ACM Transactions on Algorithms (TALG)
Throw one's cake: and eat it too
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
On the complexity of cake cutting
Discrete Optimization
Cake cutting: not just child's play
Communications of the ACM
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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 required to divide the cake fairly. It is known that O(N logN) cuts suffices, however, it is not known whether one can do better.We show that sorting can be reduced to cake-cutting: any algorithm that performs fair cake-division can sort. For a general class of cake-cutting algorithms, which we call linearly-labeled, we obtain an 驴(N log N) lower bound on their computational complexity. All the known cake-cutting algorithms fit into this general class, which leads us to conjecture that every cake-cutting algorithm is linearly-labeled. If in addition, the number of comparisons per cut is bounded (comparison-bounded algorithms), then we obtain an 驴(N log N) lower bound on the number of cuts. All known algorithms are comparison-bounded.We also study variations of envy-free cake-division, where each user feels that they have more cake than every other user. We construct utility functions for which any algorithm (including continuous algorithms) requires 驴(N2) cuts to produce such divisions. These are the the first known general lower bounds for envy-free algorithms. Finally, we study another general class of algorithms called phased algorithms, for which we show that even if one is to simply guarantee each user a piece of cake with positive value, then 驴(N log N) cuts are needed in the worst case. Many of the existing cake-cutting algorithms are phased.