Graphical evolution: an introduction to the theory of random graphs
Graphical evolution: an introduction to the theory of random graphs
Spectral bounds for the clique and independence numbers of graphs
Journal of Combinatorial Theory Series B
Does co-NP have short interactive proofs?
Information Processing Letters
The NP-completeness column: an ongoing guide
Journal of Algorithms
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
Constrained nets for graph matching and other quadratic assignment problems
Neural Computation
Relaxation labeling networks for the maximum clique problem
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Feasible and infeasible maxima in a quadratic program for maximum clique
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Evolution towards the Maximum Clique
Journal of Global Optimization
Annealed replication: a new heuristic for the maximum clique problem
Discrete Applied Mathematics
Self Annealing: Unifying Deterministic Annealing and Relaxation Labelling
EMMCVPR '97 Proceedings of the First International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A clique problem equivalent to graph isomorphism
ACM SIGACT News
A novel optimizing network architecture with applications
Neural Computation
A Lagrangian relaxation network for graph matching
IEEE Transactions on Neural Networks
Evolutionary Game Dynamics in Combinatorial Optimization: An Overview
Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
Graph-Based Methods for Vision: A Yorkist Manifesto
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Robust Point Matching for Nonrigid Shapes by Preserving Local Neighborhood Structures
IEEE Transactions on Pattern Analysis and Machine Intelligence
Payoff-Monotonic Game Dynamics and the Maximum Clique Problem
Neural Computation
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
International Journal of Computer Vision
Consensus Graphs for Symmetry Plane Estimation
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
A game-theoretic approach to partial clique enumeration
Image and Vision Computing
Kernelization of Softassign and Motzkin-Strauss Algorithms
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Inference and Validation of Networks
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
A novel neural network approach to solve exact and inexact graph isomorphism problems
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
A continuous-based approach for partial clique enumeration
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
A bound for non-subgraph isomorphism
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
A new spectral bound on the clique number of graphs
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Graph-based quadratic optimization: A fast evolutionary approach
Computer Vision and Image Understanding
Supervised learning of graph structure
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
Towards the unification of structural and statistical pattern recognition
Pattern Recognition Letters
Pattern analysis with graphs: Parallel work at Bern and York
Pattern Recognition Letters
Graph matching and clustering using kernel attributes
Neurocomputing
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We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations-a class of straightforward continuous-and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.