The complexity landscape of decompositional parameters for ILP

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Authors	GANIAN Robert ORDYNIAK Sebastian
Year of publication	2018
Type	Article in Periodical
Magazine / Source	ARTIFICIAL INTELLIGENCE
MU Faculty or unit	Faculty of Informatics
Citation
Doi	http://dx.doi.org/10.1016/j.artint.2017.12.006
Keywords	integer linear programming; treewidth; treedepth; parameterized complexity
Description	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 give an overview of the complexity of ILP w.r.t. decompositional parameters defined on the constraint matrix.
Related projects:	Highly Parallel and Distributed Computing Systems