Eiben, E., Ganian, R., Knop, D. et al. (1 more author) (2018) Unary Integer Linear Programming with Structural Restrictions. In: Lang, J., (ed.) International Joint Conferences on Artificial Intelligence Organization (IJCAI). International Joint Conferences on Artificial Intelligence Organization , 13-19 Jul 2018, Stockholm. IJCAI , pp. 1284-1290. ISBN 978-0-9992411-2-7
Abstract
Recently a number of algorithmic results have appeared which show the tractability of Integer Linear Programming (ILP) instances under strong restrictions on variable domains and/or coefficients (AAAI 2016, AAAI 2017, IJCAI 2017). In this paper, we target ILPs where neither the variable domains nor the coefficients are restricted by a fixed constant or parameter; instead, we only require that our instances can be encoded in unary. We provide new algorithms and lower bounds for such ILPs by exploiting the structure of their variable interactions, represented as a graph. Our first set of results focuses on solving ILP instances through the use of a graph parameter called clique-width, which can be seen as an extension of treewidth which also captures well-structured dense graphs. In particular, we obtain a polynomial-time algorithm for instances of bounded clique-width whose domain and coefficients are polynomially bounded by the input size, and we complement this positive result by a number of algorithmic lower bounds. Afterwards, we turn our attention to ILPs with acyclic variable interactions. In this setting, we obtain a complexity map for the problem with respect to the graph representation used and restrictions on the encoding.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2018 International Joint Conferences on Artificial Intelligence. |
Keywords: | Constraints and SAT: Dynamic Programming; Constraints and SAT: Constraint Optimisation; Heuristic Search and Game Playing: Combinatorial Search and Optimisation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 10 Aug 2018 11:42 |
Last Modified: | 19 Dec 2022 13:50 |
Published Version: | http://www.ijcai.org/proceedings/2018/179 |
Status: | Published |
Publisher: | IJCAI |
Refereed: | Yes |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133929 |