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.
@InProceedings{hrubes_et_al:LIPIcs.CCC.2021.9, author = {Hrube\v{s}, Pavel and Yehudayoff, Amir}, title = {{Shadows of Newton Polytopes}}, booktitle = {36th Computational Complexity Conference (CCC 2021)}, pages = {9:1--9:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-193-1}, ISSN = {1868-8969}, year = {2021}, volume = {200}, editor = {Kabanets, Valentine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.9}, URN = {urn:nbn:de:0030-drops-142833}, doi = {10.4230/LIPIcs.CCC.2021.9}, annote = {Keywords: Newton polytope, Monotone arithmetic circuit} }
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