Related papers: Using ILP/SAT to determine pathwidth, visibility r…
The classical, linear-time solvable Feedback Edge Set problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal…
How to draw the vertices of a complete multipartite graph $G$ on different points of a bounded $d$-dimensional integer grid, such that the sum of squared distances between vertices of $G$ is (i) minimized or (ii) maximized? For both…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP…
The rising proportion of renewable energy in the electricity mix introduces significant operational challenges for power grid operators. Effective power grid management demands adaptive decision-making strategies capable of handling dynamic…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Research on the similarity of a graph to being a tree - called the treewidth of the graph - has seen an enormous rise within the last decade, but a practically fast algorithm for this task has been discovered only recently by Tamaki (ESA…
This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
In this note, we consider the antibandwidth problem, also known as dual bandwidth problem, separation problem and maximum differential coloring problem. Given a labeled graph (i.e., a numbering of the vertices of a graph), the antibandwidth…
Given an input graph and weights on its vertices, the maximum co-2-plex problem is to find a subset of vertices maximizing the sum of their weights and inducing a graph of degree at most 1. In this article, we analyze polyhedral aspects of…
This paper proposes a novel heterogeneous grid convolution that builds a graph-based image representation by exploiting heterogeneity in the image content, enabling adaptive, efficient, and controllable computations in a convolutional…
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been…
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…
The graph invariant twin-width was recently introduced by Bonnet, Kim, Thomass\'e, and Watrigan. Problems expressible in first-order logic, which includes many prominent NP-hard problems, are tractable on graphs of bounded twin-width if a…
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…