eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
13:1
13:15
10.4230/LIPIcs.ISAAC.2021.13
article
The Complexity of Sharing a Pizza
Schnider, Patrick
1
https://orcid.org/0000-0002-2172-9285
Department of Mathematical Sciences, University of Copenhagen, Denmark
Assume you have a 2-dimensional pizza with 2n ingredients that you want to share with your friend. For this you are allowed to cut the pizza using several straight cuts, and then give every second piece to your friend. You want to do this fairly, that is, your friend and you should each get exactly half of each ingredient. How many cuts do you need?
It was recently shown using topological methods that n cuts always suffice. In this work, we study the computational complexity of finding such n cuts. Our main result is that this problem is PPA-complete when the ingredients are represented as point sets. For this, we give a new proof that for point sets n cuts suffice, which does not use any topological methods.
We further prove several hardness results as well as a higher-dimensional variant for the case where the ingredients are well-separated.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.13/LIPIcs.ISAAC.2021.13.pdf
pizza sharing
Ham-Sandwich theorem
PPA
computational geometry
computational complexity