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Computer Science > Computational Complexity

arXiv:2012.14236 (cs)
[Submitted on 28 Dec 2020 (v1), last revised 15 Jun 2023 (this version, v3)]

Title:Pizza Sharing is PPA-hard

Authors:Argyrios Deligkas, John Fearnley, Themistoklis Melissourgos
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Abstract:We study the computational complexity of finding a solution for the straight-cut and square-cut pizza sharing problems. We show that computing an $\varepsilon$-approximate solution is PPA-complete for both problems, while finding an exact solution for the square-cut problem is FIXP-hard and in BU. Our PPA-hardness results apply for any $\varepsilon < 1/5$, even when all mass distributions consist of non-overlapping axis-aligned rectangles or when they are point sets, and our FIXP-hardness result applies even when all mass distributions are unions of squares and right-angled triangles. We also prove that the decision variants of both approximate problems are NP-complete, while it is ETR-complete for the exact version of square-cut pizza sharing.
Subjects: Computational Complexity (cs.CC); Computational Geometry (cs.CG); General Topology (math.GN)
MSC classes: 91B32
Cite as: arXiv:2012.14236 [cs.CC]
  (or arXiv:2012.14236v3 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.2012.14236

Submission history

From: Themistoklis Melissourgos [view email]
[v1] Mon, 28 Dec 2020 14:10:30 UTC (2,277 KB)
[v2] Wed, 14 Jul 2021 03:15:23 UTC (2,514 KB)
[v3] Thu, 15 Jun 2023 18:25:55 UTC (1,659 KB)
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