Related papers: A structural approach to kernels for ILPs: Treewid…

We show that problems which have finite integer index and satisfy a requirement we call treewidth-bounding admit linear kernels on the class of $H$-topological-minor free graphs, for an arbitrary fixed graph $H$. This builds on earlier…

We investigate polynomial-time preprocessing for the problem of hitting forbidden minors in a graph, using the framework of kernelization. For a fixed finite set of connected graphs F, the F-Deletion problem is the following: given a graph…

We introduce a new framework for the analysis of preprocessing routines for parameterized counting problems. Existing frameworks that encapsulate parameterized counting problems permit the usage of exponential (rather than polynomial) time…

This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…

We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the…

Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…

Deep models have advanced prediction in many domains, but their lack of interpretability remains a key barrier to the adoption in many real world applications. There exists a large body of work aiming to help humans understand these black…

Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…

This paper focuses on unsupervised modeling of morphological families, collectively comprising a forest over the language vocabulary. This formulation enables us to capture edgewise properties reflecting single-step morphological…

Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…

In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing $W[1]$-hardness proofs for these problems, since XNLP-hardness implies $W[t]$-hardness for…

Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the…

We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…

It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., Vertex Cover, Feedback Vertex Set, and Triangle Packing. While there…

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…

The composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability…

Solving (mixed) integer linear programs, (M)ILPs for short, is a fundamental optimization task. While hard in general, recent years have brought about vast progress for solving structurally restricted, (non-mixed) ILPs: $n$-fold, tree-fold,…

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

We consider the ILP Feasibility problem: given an integer linear program $\{Ax = b, x\geq 0\}$, where $A$ is an integer matrix with $k$ rows and $\ell$ columns and $b$ is a vector of $k$ integers, we ask whether there exists…

Given a finite set $X$, a collection $\mathcal{T}$ of rooted phylogenetic trees on $X$ and an integer $k$, the Hybridization Number problem asks if there exists a phylogenetic network on $X$ that displays all trees from $\mathcal{T}$ and…