An Approximation Scheme For Cake Division With A Linear Number Of Cuts

In the cake cutting problem, n≥2 players want to cut a cake into n pieces so that every player gets a ‘fair’ share of the cake by his own measure.

We prove the following result: For every ε>0, there exists a cake division scheme for n players that uses at most cεn cuts, and in which each player can enforce to get a share of at least (1-ε)/n of the cake according to his own private measure.

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Correspondence to Jiří Sgall*.

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* Partially supported by Institute for Theoretical Computer Science, Prague (project LN00A056 of MŠMT ČR) and grant IAA1019401 of GA AV ČR.

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Sgall*, J., Woeginger, G.J. An Approximation Scheme For Cake Division With A Linear Number Of Cuts. Combinatorica 27, 205–211 (2007). https://doi.org/10.1007/s00493-007-0052-3

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Mathematics Subject Classification (2000):

  • 68W25
  • 90C27