### Abstract

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n - 1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation-as these terms are used in the fair-division literature-one, divide-and-conquer (D&C), minimizes the maximum number of players that any single player can envy. It works by asking n ≥ 2 players successively to place marks on a cake-valued along a line-that divide it into equal halves (when n is even) or nearly equal halves (when n is odd), then halves of these halves, and so on. Among other properties, D&C ensures players of at least 1/n shares, as they each value the cake, if and only if they are truthful. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed.

Original language | English (US) |
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Pages (from-to) | 291-307 |

Number of pages | 17 |

Journal | SIAM Review |

Volume | 53 |

Issue number | 2 |

DOIs | |

State | Published - 2011 |

### Keywords

- Binary tree
- Cake-cutting
- Fair division
- Minimal envy
- Proportional algorithm

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Mathematics
- Applied Mathematics

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## Cite this

*SIAM Review*,

*53*(2), 291-307. https://doi.org/10.1137/080729475