Shadows of Newton Polytopes
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.
Newton polytope
Monotone arithmetic circuit
Theory of computation~Algebraic complexity theory
9:1-9:23
Regular Paper
We thank Michael Forbes for pointing out the connection between shadow complexity and Conjecture 47.
Pavel
Hrubeš
Pavel Hrubeš
Institute of Mathematics, The Czech Academy of Sciences, Prague, Czech Republic
Supported by the GACR grant 19-27871X.
Amir
Yehudayoff
Amir Yehudayoff
Department of Mathematics, Technion-IIT, Haifa, Israel
10.4230/LIPIcs.CCC.2021.9
Pavel Hrubeš and Amir Yehudayoff
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode