Pizza Sharing is PPA-hard

Deligkas, Argyrios, Fearnley, John and Melissourgos, Themistoklis
Pizza Sharing is PPA-hard.

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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 show that decision variants of the square-cut problem are hard: we show that the approximate problem is NP-complete, and the exact problem is ETR-complete.

Item Type: Article
Uncontrolled Keywords: cs.CC, cs.CC, cs.CG, math.GN
Depositing User: Symplectic Admin
Date Deposited: 15 Jan 2021 09:24
Last Modified: 21 Jul 2021 11:10
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