Corpus ID: 119129982

The Muffin Problem

@inproceedings{Cui2017TheMP,
  title={The Muffin Problem},
  author={Guangiqi Cui and John Dickerson and Naveen Durvasula and William Gasarch and Erik Metz and Jacob Prinz and Naveen Raman and Daniel Smolyak and Sung Hyun Yoo},
  year={2017}
}
  • Guangiqi Cui, John Dickerson, +6 authors Sung Hyun Yoo
  • Published 2017
  • Mathematics
  • You have $m$ muffins and $s$ students. You want to divide the muffins into pieces and give the shares to students such that every student has $\frac{m}{s}$ muffins. Find a divide-and-distribute protocol that maximizes the minimum piece. Let $f(m,s)$ be the minimum piece in the optimal protocol. We prove that $f(m,s)$ exists, is rational, and finding it is computable (though possibly difficult). We show that $f(m,s)$ can be derived from $f(s,m)$; hence we need only consider $m\ge s$. We give a… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Citations

    Publications citing this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-7 OF 7 REFERENCES

    A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents

    • Haris Aziz, Simon Mackenzie
    • Computer Science, Mathematics
    • 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
    • 2016
    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    Cake cutting really is not a piece of cake

    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    Cake-cutting algorithms - be fair if you can

    VIEW 1 EXCERPT
    HIGHLY INFLUENTIAL

    Fair division - from cake-cutting to dispute resolution

    VIEW 1 EXCERPT
    HIGHLY INFLUENTIAL

    An Envy-Free Cake Division Protocol

    VIEW 1 EXCERPT
    HIGHLY INFLUENTIAL

    A note on cake cutting

    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    Described to Jeremy Copeland and in the New York Times Numberplay Online Blog wordplay.blogs.nytimes.com/2013/08/19/cake

    • A. Frank
    • The muffin problem,
    • 2013
    VIEW 2 EXCERPTS