License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2021.9
URN: urn:nbn:de:0030-drops-142833
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14283/
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HrubeŇ°, Pavel ; Yehudayoff, Amir

Shadows of Newton Polytopes

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LIPIcs-CCC-2021-9.pdf (0.7 MB)


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}
}

Keywords: Newton polytope, Monotone arithmetic circuit
Collection: 36th Computational Complexity Conference (CCC 2021)
Issue Date: 2021
Date of publication: 08.07.2021


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