An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stereo Correspondence Through Feature Grouping and Maximal Cliques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Relaxation labeling networks for the maximum clique problem
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Structural Matching by Discrete Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
On a relation between graph edit distance and maximum common subgraph
Pattern Recognition Letters
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
Quantum Factoring, Discrete Logarithms, and the Hidden Subgroup Problem
Computing in Science and Engineering
Structural Matching in Computer Vision Using Probabilistic Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Graph Edit Distance from Spectral Seriation
IEEE Transactions on Pattern Analysis and Machine Intelligence
The hidden subgroup problem and permutation group theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Exact and Approximate Graph Matching Using Random Walks
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph spectral image smoothing using the heat kernel
Pattern Recognition
Physically-motivated dynamical algorithms for the graph isomorphism problem
Quantum Information & Computation
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Organization of Relational Models for Scene Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph matching using the interference of discrete-time quantum walks
Image and Vision Computing
Indexing of 3d models based on graph of surfacic regions
Proceedings of the ACM workshop on 3D object retrieval
Graph Kernels from the Jensen-Shannon Divergence
Journal of Mathematical Imaging and Vision
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We consider how continuous-time quantum walks can be used for graph matching. We focus in detail on both exact and inexact graph matching, and consider in depth the problem of measuring graph similarity. We commence by constructing an auxiliary graph, in which the two graphs to be matched are co-joined by a layer of indicator vertices (one for each potential correspondence between a pair of vertices). We simulate a continuous-time quantum walk in parallel on the two graphs. The layer of connecting indicator vertices in the auxiliary graph allow quantum interference to take place between the two walks. The interference amplitudes on the indicator vertices are determined by differences in the two walks, and can be used to calculate probabilities for matches between pairs of vertices from the graphs. By applying the Hungarian (Kuhn-Munkres) algorithm to these probabilities, we recover a correspondence mapping between the graphs. To calculate graph similarity, we combine these probabilities with edge-consistency information to give a consistency measure. Based on the consistency measure, we define two graph similarity measures, one of which requires correspondence matches while the second does not. We analyse our approach experimentally using synthetic and real-world graphs. This reveals that our method gives results that are intermediate between the most sophisticated iterative techniques available, and simpler less complex ones.