The Complexity Landscape of Decompositional Parameters for ILP

D 2016

The Complexity Landscape of Decompositional Parameters for ILP

GANIAN, Robert and Sebastian ORDYNIAK

Basic information

Original name

The Complexity Landscape of Decompositional Parameters for ILP

Authors

GANIAN, Robert (203 Czech Republic, guarantor, belonging to the institution) and Sebastian ORDYNIAK (276 Germany)

Edition

USA, Proceedings of the Thirtieth {AAAI} Conference on Artificial Intelligence, p. 710-716, 7 pp. 2016

Publisher

AAAI Press

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/00216224:14330/16:00093940

Organization unit

Faculty of Informatics

ISBN

978-1-57735-760-5

Keywords in English

ILP; treewidth

Abstract

V originále

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.

Citovat

GANIAN, Robert and Sebastian ORDYNIAK. The Complexity Landscape of Decompositional Parameters for ILP. Online. In Dale Schuurmans, Michael P. Wellman. Proceedings of the Thirtieth {AAAI} Conference on Artificial Intelligence. USA: AAAI Press, 2016, p. 710-716. ISBN 978-1-57735-760-5.

@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 and 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, p.~710-716. ISBN~978-1-57735-760-5.

Detailed Information on Publication Record