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 …

The theory of $ n $-fold integer programming has been recently emerging as an important
tool in parameterized complexity. The input to an $ n $-fold integer program (IP) consists of …

For problems intractable on graphs of bounded treewidth, two graph parameters treedepth
and vertex cover number have been used to obtain fine-grained algorithmic and complexity …

We consider the standard ILP Feasibility problem: given an integer linear program of the
form {A x= b, x⩾ 0}, where A is an integer matrix with k rows and ℓ columns, x is a vector of ℓ …

Powerful results from the theory of integer programming have recently led to substantial
advances in parameterized complexity. However, our perception is that, except for Lenstra's …

A classic result of Lenstra [Math. Oper. Res. 1983] says that an integer linear program can
be solved in fixed-parameter tractable (FPT) time for the parameterization by the number of …

Abstract We study Steiner Forest on H-subgraph-free graphs, that is, graphs that do not
contain some fixed graph H as a (not necessarily induced) subgraph. We are motivated by a …

Vertex Integrity is a graph measure which sits squarely between two more well-studied
notions, namely vertex cover and tree-depth, and that has recently gained attention as a …

Abstract 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 …

A long line of research on fixed parameter tractability of integer programming culminated
with showing that integer programs with n variables and a constraint matrix with dual tree …