Shadows of Newton Polytopes

Authors Pavel Hrubeš, Amir Yehudayoff

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Author Details

Pavel Hrubeš
  • Institute of Mathematics, The Czech Academy of Sciences, Prague, Czech Republic
Amir Yehudayoff
  • Department of Mathematics, Technion-IIT, Haifa, Israel


We thank Michael Forbes for pointing out the connection between shadow complexity and Conjecture 47.

Cite AsGet BibTex

Pavel Hrubeš and Amir Yehudayoff. Shadows of Newton Polytopes. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We define the shadow complexity of a polytope P as the maximum number of vertices in a linear projection of P to the plane. We describe connections to algebraic complexity and to parametrized optimization. We also provide several basic examples and constructions, and develop tools for bounding shadow complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic complexity theory
  • Newton polytope
  • Monotone arithmetic circuit


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