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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,…
Given two graphs $H$ and $G$, the Subgraph Isomorphism problem asks if $H$ is isomorphic to a subgraph of $G$. While NP-hard in general, algorithms exist for various parameterized versions of the problem: for example, the problem can be…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
It is well known that the spectrum and the Smith normal form of a matrix can be computed in polynomial time. Thus, it is interesting to explore how good are these parameters for distinguishing graphs. This is relevant since it is related to…
In this paper we explore whether or not deep neural architectures can learn to classify Boolean satisfiability (SAT). We devote considerable time to discussing the theoretical properties of SAT. Then, we define a graph representation for…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
This paper presents an advanced DAG-based algorithm for datapath synthesis that targets area minimization using logic-level resource sharing. The problem of identifying common specification logic is formulated using unweighted graph…
The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper…
Graph association rule mining is a data mining technique used for discovering regularities in graph data. In this study, we propose a novel concept, {\it path association rule mining}, to discover the correlations of path patterns that…
Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…
Heterogeneous graphs have multiple node and edge types and are semantically richer than homogeneous graphs. To learn such complex semantics, many graph neural network approaches for heterogeneous graphs use metapaths to capture multi-hop…
Binary Code Similarity Detection (BCSD) is not only essential for security tasks such as vulnerability identification but also for code copying detection, yet it remains challenging due to binary stripping and diverse compilation…
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is…
This study poses the feature correspondence problem as a hypergraph node labeling problem. Candidate feature matches and their subsets (usually of size larger than two) are considered to be the nodes and hyperedges of a hypergraph. A…
A wide range of graph learning tasks, such as structure discovery, temporal graph analysis, and combinatorial optimization, focus on inferring graph structures from data, rather than making predictions on given graphs. However, the…
Graph matching is an important problem that has received widespread attention, especially in the field of computer vision. Recently, state-of-the-art methods seek to incorporate graph matching with deep learning. However, there is no…