Pizza Sharing Is PPA-Hard

No. 5: AAAI-22 Technical Tracks 5

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 36

AAAI Technical Track on Game Theory and Economic Paradigms

We study the computational complexity of computing solutions for the straight-cut and square-cut pizza sharing problems. We show that finding an approximate solution is PPA-hard for the straight-cut problem, and PPA-complete for the square-cut problem, while finding an exact solution for the square-cut problem is FIXP-hard and in BU. Our PPA-hardness results apply even when all mass distributions are unions of non-overlapping squares, and our FIXP-hardness result applies even when all mass distributions are unions of weighted squares and right-angled triangles. We also prove that decision variants of the square-cut problem are hard: the approximate problem is NP-complete, and the exact problem is ETR-complete.

10.1609/aaai.v36i5.20426