Cake cutting really is not a piece of cake
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Confidently Cutting a Cake into Approximately Fair Pieces
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Cake cutting: not just child's play
Communications of the ACM
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Given a heterogeneous cake and 5 players, we give the first bounded algorithm for computing an envy-free division of the cake, such that each person thinks he gets the largest piece. The case with 4 players was solved in a famous paper by Brams et al. in 1997. Our algorithm can be discretized to obtain an *** envy-free division in $O({\rm polylog} \left( 1 / \epsilon \right))$ time. The algorithm is based on augmenting the irrevocable advantage graph in a new way. We also look at the open problem of finding discrete procedures for computing envy-free division among 4 players. We present a simple algorithm that finds an envy-free division of a portion of the cake, such that each player gets at least 1/4 of the whole cake (in his valuation).