On August 5, 2020, Robert Ganian from Technische Universität Wien gave an online talk giving an overview of recent approaches to the integer linear programming based on the structural analysis of graphs associated with the instances at the Virtual Discrete Math Colloquium. The title of his talk was “Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions“.
Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science. ILP is NP-complete, and until recently we have lacked a systematic study of the complexity of ILP through the lens of variable-constraint interactions. This changed drastically in recent years thanks to a series of results that together lay out a detailed complexity landscape for the problem centered around the structure of graphical representations of instances. The aim of this talk is to summarize these recent developments and put them into context. Special attention will be paid to the structural parameter treedepth, and at the end of the talk we will also consider how treedepth can be used to design algorithms for problems beyond ILP.
