Publication details

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

Authors

DVORAK Pavel EIBEN Eduard GANIAN Robert KNOP Dusan ORDYNIAK Sebastian

Type Article in Proceedings
Conference Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017
MU Faculty or unit

Faculty of Informatics

Citation
WWW https://www.ijcai.org/proceedings/2017/85
Doi http://dx.doi.org/10.24963/ijcai.2017/85
Keywords Integer Linear Programming; Backdoors; Parameterized Algorithms
Description 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.

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