Related papers: A Novel Approach to Complex Problems
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we apply it to the NP complete problem of finding the largest perfect clique within a graph $G$.
A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…
Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
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…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
Subgraph queries also known as subgraph isomorphism search is a fundamental problem in querying graph-like structured data. It consists to enumerate the subgraphs of a data graph that match a query graph. This problem arises in many…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
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…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…
Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how Graph Neural Networks (GNN), which have emerged as an effective model for various…
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…