License: 
Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2482
URN: urn:nbn:de:0030-drops-24826
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2482/
Kowalczyk, Michael ;
Cai, Jin-Yi
Holant Problems for Regular Graphs with Complex Edge Functions
Abstract
We prove a complexity dichotomy theorem for Holant Problems on $3$-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted Pairs, which allow us to prove that a pair of combinatorial gadgets \emph{in combination} succeed in proving \#P-hardness; and (3) algebraic symmetrization, which significantly lowers the \emph{symbolic complexity} of the proof for computational complexity. With \emph{holographic reductions} the classification theorem also applies to problems beyond the basic model.
BibTeX - Entry
@InProceedings{kowalczyk_et_al:LIPIcs:2010:2482,
author = {Michael Kowalczyk and Jin-Yi Cai},
title = {{Holant Problems for Regular Graphs with Complex Edge Functions}},
booktitle = {27th International Symposium on Theoretical Aspects of Computer Science},
pages = {525--536},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-16-3},
ISSN = {1868-8969},
year = {2010},
volume = {5},
editor = {Jean-Yves Marion and Thomas Schwentick},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2010/2482},
URN = {urn:nbn:de:0030-drops-24826},
doi = {10.4230/LIPIcs.STACS.2010.2482},
annote = {Keywords: Computational complexity}
}
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Keywords: |
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Computational complexity |
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Collection: |
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27th International Symposium on Theoretical Aspects of Computer Science |
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Issue Date: |
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2010 |
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Date of publication: |
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09.03.2010 |
