Related papers: On spectral properties for graph matching and grap…
Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
Semidefinite programs are generally challenging to solve due to their high dimensionality. Burer and Monteiro developed a non-convex approach to solve linear SDP problems by applying its low rank property. Their approach is fast because…
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 propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
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…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
Graph matching is one of the most important problems in graph theory and combinatorial optimization, with many applications in various domains. Although meta-heuristic algorithms have had good performance on many NP-Hard and NP-Complete…
The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…
Extracting structured subgraphs inside large graphs - often known as the planted subgraph problem - is a fundamental question that arises in a range of application domains. This problem is NP-hard in general, and as a result, significant…
This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism $f$, an \( f \)-compatible matrices capture aspects of the symmetry, represented…
We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…
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…
The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
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…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…