Solving Integer Linear Programs with a Small Number of Global Variables and Constraints

Pavel Dvorak, Eduard Eiben, Robert Ganian, Dusan Knop, Sebastian Ordyniak

Research output: Contribution to conferencePaperpeer-review


Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable. Here we study ILP instances consisting of a small number of "global'' variables and/or constraints such that the remaining part of the instance consists of small and otherwise independent components; this is captured in terms of a structural measure we call fracture backdoors which generalizes, for instance, the well-studied class of N-fold ILP instances. Our main contributions can be divided into three parts. First, we formally develop fracture backdoors and obtain exact and approximation algorithms for computing these. Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints in the instance. Finally, we complement the developed algorithms with matching lower bounds. Altogether, our results paint a near-complete complexity landscape of ILP with respect to fracture backdoors.
Original languageEnglish
Number of pages7
Publication statusPublished - 2017
EventTwenty-Sixth International Joint Conference on Artificial Intelligence - Melbourne, Australia
Duration: 19 Aug 201725 Aug 2017


ConferenceTwenty-Sixth International Joint Conference on Artificial Intelligence
Abbreviated titleIJCAI 2017
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