Eiben, E, Ganian, R, Knop, D et al. (3 more authors) (2019) Integer Programming and Incidence Treedepth. In: Lecture Notes in Computer Science. IPCO 2019: Integer Programming and Combinatorial Optimization, 22-24 May 2019, Ann Arbor, MI, USA. Springer Verlag , pp. 194-204. ISBN 9783030179526
Abstract
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming is fixed-parameter tractable with respect to the primal (or dual) treedepth of the Gaifman graph of its constraint matrix and the largest coefficient (in absolute value). Motivated by this, Koutecký, Levin, and Onn [ICALP 2018] asked whether it is possible to extend these result to a more broader class of integer linear programs. More formally, is integer linear programming fixed-parameter tractable with respect to the incidence treedepth of its constraint matrix and the largest coefficient (in absolute value)?
We answer this question in negative. We prove that deciding the feasibility of a system in the standard form, Ax=b,l≤x≤u , is NP-hard even when the absolute value of any coefficient in A is 1 and the incidence treedepth of A is 5. Consequently, it is not possible to decide feasibility in polynomial time even if both the assumed parameters are constant, unless P=NP .
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2019. This is an author produced version of a conference paper published in Lecture Notes in Computer Science . Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Integer programming; Incidence treedepth; Gaifman graph; Computational complexity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Nov 2020 15:54 |
Last Modified: | 17 Nov 2020 15:54 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/978-3-030-17953-3_15 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:168080 |