The complexity landscape of decompositional parameters for ILP: Programs with few global variables and constraints

Integer Linear Programming (ILP) has a broad range of applications in various areas artificial intelligence. Yet spite recent advances, we still lack thorough understanding which structural restrictions make ILP tractable. Here study instances consisting small number “global” variables and/or constraints such that the remaining part instance consists and otherwise independent components; this is captured terms measure call fracture backdoors generalizes, for instance, well-studied class N-fold instances. Our main contributions can be divided into three parts. First, formally develop obtain exact approximation algorithms computing these. Second, exploit these to several new parameterized ILP; performance will naturally scale based on global or instance. Finally, complement developed with matching lower bounds. Altogether, our results paint near-complete complexity landscape respect backdoors.1