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Open AccessArticle

Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions: A Survey

1
Institute of Logic and Computation, Vienna University of Technology, 1040 Vienna, Austria
2
Department of Computer Science, University of Sheffield, Western Bank, Sheffield S10 2TN, UK
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Authors to whom correspondence should be addressed.
Algorithms 2019, 12(12), 248; https://doi.org/10.3390/a12120248
Received: 29 September 2019 / Revised: 6 November 2019 / Accepted: 20 November 2019 / Published: 22 November 2019
(This article belongs to the Special Issue New Frontiers in Parameterized Complexity and Algorithms)
Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science. ILP is NP-complete, and until recently we have lacked a systematic study of the complexity of ILP through the lens of variable-constraint interactions. This changed drastically in recent years thanks to a series of results that together lay out a detailed complexity landscape for the problem centered around the structure of graphical representations of instances. The aim of this survey is to summarize these recent developments, put them into context and a unified format, and make them more approachable for experts from many diverse backgrounds. View Full-Text
Keywords: integer linear programming; parameterized complexity; treewidth; treedepth integer linear programming; parameterized complexity; treewidth; treedepth
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Ganian, R.; Ordyniak, S. Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions: A Survey. Algorithms 2019, 12, 248.

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