Arising from structural graph theory, treewidth has become a focus of study in fixed-
parameter tractable algorithms. Many NP-hard problems are known to be solvable in O (n· 2 …

We consider fundamental algorithmic number theoretic problems and their relation to a class
of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage …

We study the general integer programming problem where the number of variables n is a
variable part of the input. We consider two natural parameters of the constraint matrix A: its …

We consider box-constrained integer programs with objective g (W x)+ c T x, where g is a
“complicated” function with an m dimensional domain. Here we assume we have n≫ m …

An intensive line of research on fixed parameter tractability of integer programming is
focused on exploiting the relation between the sparsity of a constraint matrix $ A $ and the …

In spite of the fundamental role of neural networks in contemporary machine learning
research, our understanding of the computational complexity of optimally training neural …

An intensive line of research on fixed parameter tractability of integer programming is
focused on exploiting the relation between the sparsity of a constraint matrix A and the norm …

We provide several novel algorithms and lower bounds in central settings of mixed-integer
(non-) linear optimization, shedding new light on classic results in the field. This includes an …

A backdoor in a finite-domain CSP instance is a set of variables where each possible
instantiation moves the instance into a polynomial-time solvable class. Backdoors have …

This thesis focuses on algorithmic questions arising from discrete mathematics, with a
particular emphasis on optimization on planar graphs. Historically, research in this area …