The NCI drug information system. 1. System overview
Journal of Chemical Information & Computer Sciences
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
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
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
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
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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
Edit Distance From Graph Spectra
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Graph Edit Distance from Spectral Seriation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact and Approximate Graph Matching Using Random Walks
IEEE Transactions on Pattern Analysis and Machine Intelligence
Protein function prediction via graph kernels
Bioinformatics
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A tutorial on spectral clustering
Statistics and Computing
The Representation and Matching of Pictorial Structures
IEEE Transactions on Computers
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
A random walk kernel derived from graph edit distance
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Robust multi-body motion tracking using commute time clustering
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
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
Journal of Biomedical Informatics
Graph Kernels from the Jensen-Shannon Divergence
Journal of Mathematical Imaging and Vision
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In this paper, we consider how discrete-time quantum walks can be applied to graph-matching problems. The matching problem is abstracted using an auxiliary graph that connects pairs of vertices from the graphs to be matched by way of auxiliary vertices. A discrete-time quantum walk is simulated on this auxiliary graph and the quantum interference on the auxiliary vertices indicates possible matches. When dealing with graphs for which there is no exact match, the interference amplitudes together with edge consistencies are used to define a consistency measure. We also explore the use of the method for inexact graph-matching problems. We have tested the algorithm on graphs derived from the NCI molecule database and found it to significantly reduce the space of possible permutation matchings, typically by a factor of 10^-^2^0-10^-^3^0, thereby allowing the graphs to be matched directly. An analysis of the quantum walk in the presence of structural errors between graphs is used as the basis of the consistency measure. We test the performance of this measure on graphs derived from images in the COIL-100 database.