The Complexity Landscape of Decompositional Parameters for ILP

Authors

  • Robert Ganian Technische Universität Wien
  • Sebastian Ordyniak Technische Universität Wien

DOI:

https://doi.org/10.1609/aaai.v30i1.10078

Keywords:

integer linear programming, treedepth and treewidth, parameterized complexity, complexity landscape

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.

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Published

2016-02-21

How to Cite

Ganian, R., & Ordyniak, S. (2016). The Complexity Landscape of Decompositional Parameters for ILP. Proceedings of the AAAI Conference on Artificial Intelligence, 30(1). https://doi.org/10.1609/aaai.v30i1.10078

Issue

Section

Technical Papers: Heuristic Search and Optimization