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@inproceedings{1376002,
author = {Ganian, Robert and Ordyniak, Sebastian},
address = {USA},
booktitle = {Proceedings of the Thirtieth {AAAI} Conference on Artificial Intelligence},
editor = {Dale Schuurmans, Michael P. Wellman},
keywords = {ILP; treewidth},
howpublished = {elektronická verze "online"},
language = {eng},
location = {USA},
isbn = {978-1-57735-760-5},
pages = {710-716},
publisher = {AAAI Press},
title = {The Complexity Landscape of Decompositional Parameters for ILP},
url = {https://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12432},
year = {2016}
}
TY - JOUR
ID - 1376002
AU - Ganian, Robert - Ordyniak, Sebastian
PY - 2016
TI - The Complexity Landscape of Decompositional Parameters for ILP
PB - AAAI Press
CY - USA
SN - 9781577357605
KW - ILP
KW - treewidth
UR - https://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12432
N2 - Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range of applications, only few tractable fragments of ILP are known, probably the most prominent of which is based on the notion of total unimodularity. Using entirely different techniques, we identify new tractable fragments of ILP by studying structural parameterizations of the constraint matrix within the framework of parameterized complexity. In particular, we show that ILP is fixed-parameter tractable when parameterized by the treedepth of the constraint matrix and the maximum absolute value of any coefficient occurring in the ILP instance. Together with matching hardness results for the more general parameter treewidth, we draw a detailed complexity landscape of ILP w.r.t. decompositional parameters defined on the constraint matrix.
ER -
GANIAN, Robert a Sebastian ORDYNIAK. The Complexity Landscape of Decompositional Parameters for ILP. Online. In Dale Schuurmans, Michael P. Wellman. \textit{Proceedings of the Thirtieth $\{$AAAI$\}$ Conference on Artificial Intelligence}. USA: AAAI Press, 2016, s.~710-716. ISBN~978-1-57735-760-5.
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