The Complexity Landscape of Decompositional Parameters for ILP

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.

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

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• Publication form: electronic version available online
• WWW: 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
• Tags: core_A, firank_1
• Tags: International impact, Reviewed

Abstract

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.