Introduction to algorithms
Cake cutting really is not a piece of cake
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the complexity of cake cutting
Discrete Optimization
On Low-Envy Truthful Allocations
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Degrees of Guaranteed Envy-Freeness in Finite Bounded Cake-Cutting Protocols
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
The Efficiency of Fair Division
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
The efficiency of fair division with connected pieces
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Throw one's cake: and eat it too
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Towards more expressive cake cutting
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Cake cutting: not just child's play
Communications of the ACM
Computing socially-efficient cake divisions
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
No agent left behind: dynamic fair division of multiple resources
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The problem of fairly dividing a cake (as a metaphor for a heterogeneous divisible good) has been the subject of much interest since the 1940's, and is of importance in multiagent resource allocation. Two fairness criteria are usually considered: proportionality, in the sense that each of the n agents receives at least 1/n of the cake; and the stronger property of envy-freeness, namely that each agent prefers its own piece of cake to the others' pieces. For proportional division, there are algorithms that require O(n log n) steps, and recent lower bounds imply that one cannot do better. In stark contrast, known (discrete) algorithms for envy-free division require an unbounded number of steps, even when there are only four agents. In this paper, we give an Ω(n2) lower bound for the number of steps required by envy-free cake-cutting algorithms. This result provides, for the first time, a true separation between envy-free and proportional division, thus giving a partial explanation for the notorious difficulty of the former problem.