Abstract
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.
BibTeX - Entry
@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/opus/volltexte/2021/14283},
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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Keywords: |
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Newton polytope, Monotone arithmetic circuit |
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Collection: |
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36th Computational Complexity Conference (CCC 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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08.07.2021 |
Creative Commons Attribution 4.0 International license (CC BY 4.0)