Related papers: SAT-Based Algorithms for Regular Graph Pattern Mat…
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
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…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
The Conway-99 problem questions the existence of a strongly regular graph with 99 vertices and specific parameters. A \textit{strongly} regular graph is a regular graph that exhibits two additional properties: vertices must share a fixed…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
Graph classification aims to categorize graphs based on their structural and attribute features, with applications in diverse fields such as social network analysis and bioinformatics. Among the methods proposed to solve this task, those…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
Edge-labeled graphs are widely used to describe relationships between entities in a database. Given a query subgraph that represents an example of what the user is searching for, we study the problem of efficiently searching for similar…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
Repetitive DNA (repeats) poses significant challenges for accurate and efficient genome assembly and sequence alignment. This is particularly true for metagenomic data, where genome dynamics such as horizontal gene transfer, gene…
Machine learning models that can exploit the inherent structure in data have gained prominence. In particular, there is a surge in deep learning solutions for graph-structured data, due to its wide-spread applicability in several fields.…
We claimed that there is a polynomial algorithm to test if two graphs are isomorphic. But the algorithm is wrong. It only tests if the adjacency matrices of two graphs have the same eigenvalues. There is a counterexample of two…
Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…
A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
An $H$-graph is an intersection graph of connected subgraphs of a suitable subdivision of a fixed graph $H$. Many important classes of graphs, including interval graphs, circular-arc graphs, and chordal graphs, can be expressed as…