Related papers: Graph Partitioning with Acyclicity Constraints
Graph clustering is a central topic in unsupervised learning with a multitude of practical applications. In recent years, multi-view graph clustering has gained a lot of attention for its applicability to real-world instances where one has…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
In this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data…
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split…
We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…
The Minimum Path Cover (MPC) problem consists of finding a minimum-cardinality set of node-disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on acyclic digraphs (DAGs) where, given a subset of…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…
Graph Generating Dependencies (GGDs) informally express constraints between two (possibly different) graph patterns which enforce relationships on both graph's data (via property value constraints) and its structure (via topological…
The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
Convolutional graph networks are used in particle physics for effective event reconstructions and classifications. However, their performances can be limited by the considerable amount of sensors used in modern particle detectors if applied…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…
A common approach to scaling transactional databases in practice is horizontal partitioning, which increases system scalability, high availability and self-manageability. Usu- ally it is very challenging to choose or design an optimal…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
We study the problem of partitioning the edge set of the complete graph into bipartite subgraphs under certain constraints defined by forbidden subgraphs. These constraints lead to both classical problems, such as partitioning into…