Related papers: A Heuristic for Direct Product Graph Decomposition
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
A directed graph $G=(V,E)$ is twinless strongly connected if it contains a strongly connected spanning subgraph without any pair of antiparallel (or twin) edges. The twinless strongly connected components (TSCCs) of a directed graph $G$ are…
In matching theory, one of the most fundamental and classical branches of combinatorics, {\em canonical decompositions} of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities. In this work, we propose a novel approach for the partitioning…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromatic number of some Cartesian products. One of our main…
Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the…
We study embeddings of graphs with bounded treewidth or bounded simple treewidth into the undirected graph underlying the directed product of two directed graphs. If the factors have bounded maximum indegrees, then the product graph has…
We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
Graphical calculus is an intuitive visual notation for manipulating tensors and index contractions. Using graphical calculus leads to simple and memorable derivations, and with a bit of practice one can learn to prove complex identities…
The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant "approximate" prime factorization, is the development of local approaches that…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
We demonstrate that a single training trajectory can transform a graph neural network into an unsupervised heuristic for combinatorial optimization. Focusing on the Travelling Salesman Problem, we show that encoding global structural…