Related papers: A Novel Approach to Complex Problems
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
We study the imbalance problem on complete bipartite graphs. The imbalance problem is a graph layout problem and is known to be NP-complete. Graph layout problems find their applications in the optimization of networks for parallel computer…
In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search.…
Graph neural networks provide a powerful toolkit for embedding real-world graphs into low-dimensional spaces according to specific tasks. Up to now, there have been several surveys on this topic. However, they usually lay emphasis on…
In recent years, machine learning and deep learning approaches such as artificial neural networks have gained in popularity for the resolution of automatic puzzle resolution problems. Indeed, these methods are able to extract high-level…
Subgraph matching is to find all subgraphs in a data graph that are isomorphic to an existing query graph. Subgraph matching is an NP-hard problem, yet has found its applications in many areas. Many learning-based methods have been proposed…
As one of the most fundamental tasks in graph theory, subgraph matching is a crucial task in many fields, ranging from information retrieval, computer vision, biology, chemistry and natural language processing. Yet subgraph matching problem…
Image matching is a key component of many tasks in computer vision and its main objective is to find correspondences between features extracted from different natural images. When images are represented as graphs, image matching boils down…
Graph Neural Networks (GNNs) are a form of deep learning that enable a wide range of machine learning applications on graph-structured data. The learning of GNNs, however, is known to pose challenges for memory-constrained devices such as…
As large-scale graphs become more widespread, more and more computational challenges with extracting, processing, and interpreting large graph data are being exposed. It is therefore natural to search for ways to summarize these expansive…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a…
In this work we consider a straightforward linear programming formulation of the recently introduced $\{k\}$-packing function problem in graphs, for each fixed value of the positive integer number $k$. We analyse a special relation between…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
An attempt of a new kind of complexity anthropology is considered.
Graph Neural Networks (GNNs) have emerged as the de facto standard for modeling graph data, with attention mechanisms and transformers significantly enhancing their performance on graph-based tasks. Despite these advancements, the…
In this paper we provide a principled approach to solve a transductive classification problem involving a similar graph (edges tend to connect nodes with same labels) and a dissimilar graph (edges tend to connect nodes with opposing…
Graph anomaly detection (GAD), which aims to identify unusual graph instances (nodes, edges, subgraphs, or graphs), has attracted increasing attention in recent years due to its significance in a wide range of applications. Deep learning…
Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common…
Knowledge graphs have gained popularity for their ability to organize and analyze complex data effectively. When combined with graph embedding techniques, such as graph neural networks (GNNs), knowledge graphs become a potent tool in…