DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP and Sebastian ORDYNIAK. Solving Integer Linear Programs with a Small Number of Global Variables and Constraints. Online. In Carles Sierra. Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017. USA: ijcai.org, 2017, p. 607-613. ISBN 978-0-9992411-0-3. Available from: https://dx.doi.org/10.24963/ijcai.2017/85.
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Basic information
Original name Solving Integer Linear Programs with a Small Number of Global Variables and Constraints
Authors DVORAK, Pavel (203 Czech Republic), Eduard EIBEN (703 Slovakia), Robert GANIAN (203 Czech Republic, guarantor, belonging to the institution), Dusan KNOP (203 Czech Republic) and Sebastian ORDYNIAK (40 Austria).
Edition USA, Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017, p. 607-613, 7 pp. 2017.
Publisher ijcai.org
Other information
Original language English
Type of outcome Proceedings paper
Field of Study 10200 1.2 Computer and information sciences
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/00216224:14330/17:00100548
Organization unit Faculty of Informatics
ISBN 978-0-9992411-0-3
ISSN 1045-0823
Doi http://dx.doi.org/10.24963/ijcai.2017/85
UT WoS 000764137500085
Keywords in English Integer Linear Programming; Backdoors; Parameterized Algorithms
Tags core_A, firank_1
Tags International impact, Reviewed
Changed by Changed by: Mgr. Michal Petr, učo 65024. Changed: 16/5/2022 15:49.
Abstract
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable. Here we study ILP instances consisting of a small number of ``global'' variables and/or constraints such that the remaining part of the instance consists of small and otherwise independent components; this is captured in terms of a structural measure we call fracture backdoors which generalizes, for instance, the well-studied class of N-fold ILP instances. Our main contributions can be divided into three parts. First, we formally develop fracture backdoors and obtain exact and approximation algorithms for computing these. Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints in the instance. Finally, we complement the developed algorithms with matching lower bounds. Altogether, our results paint a near-complete complexity landscape of ILP with respect to fracture backdoors.
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