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arXiv · 1510.02132

Discrete Envy-free Division of Necklaces and Maps

Roberto Barrera·Kathryn Nyman·Amanda Ruiz·Francis Edward Su·Yan X. Zhang
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Abstract

We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible "cake" with a necklace of discrete, indivisible "beads." We focus specifically on envy-free divisions, exploring different constraints on player-preferences. We show we usually cannot guarantee an envy-free division and consider situations where we can obtain an envy-free division for relatively small. We also prove a 2-dimensional result with a grid of indivisible objects. This may be viewed as a way to divide a state with indivisible districts among a set of constituents, producing somewhat gerrymandered regions that form an envy-free division of the state.

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Roberto Barrera, Kathryn Nyman, Amanda Ruiz, Francis Edward Su, Yan X. Zhang. 2017-10-12. Discrete Envy-free Division of Necklaces and Maps. https://arxiv.org/abs/1510.02132

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