Algorithmic Solutions for Envy-Free Cake Cutting
نویسندگان
چکیده
We study the problem of finding an envy-free allocation of a cake to d+1 players using d cuts. Two models are considered, namely, the oracle-function model and the polynomial-time function model. In the oracle-function model, we are interested in the number of times an algorithm has to query the players about their preferences to find an allocation with the envy less than . We derive a matching lower and upper bound of 41/ 5d−1 for players with Lipschitz utilities and any d > 1. In the polynomial-time function model, where the utility functions are given explicitly by polynomial-time algorithms, we show that the envy-free cake-cutting problem has the same complexity as finding a Brouwer’s fixed point, or, more formally, it is PPAD-complete. On the flip side, for monotone utility functions, we propose a fully polynomial-time algorithm (FPTAS) to find an approximate envy-free allocation of a cake among three people using two cuts.
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ورودعنوان ژورنال:
- Operations Research
دوره 60 شماره
صفحات -
تاریخ انتشار 2012