“Evolutionary” selection dynamics in games: convergence and limit properties
International Journal of Game Theory
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
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
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Approximating maximum clique with a Hopfield network
IEEE Transactions on Neural Networks
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
On aggregation issues in spatial data management
ADC '02 Proceedings of the 13th Australasian database conference - Volume 5
Global Escape Strategies for Maximizing QuadraticForms over a Simplex
Journal of Global Optimization
On Standard Quadratic Optimization Problems
Journal of Global Optimization
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
On solving the maximum clique problem
Journal of Global Optimization
Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Annealed replication: a new heuristic for the maximum clique problem
Discrete Applied Mathematics
Evolutionary Game Dynamics in Combinatorial Optimization: An Overview
Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
Detecting Functionally Coherent Networks in fMRI Data of the Human Brain Using Replicator Dynamics
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
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
A Complementary Pivoting Approach to Graph Matching
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Pattern Recognition Letters - Special issue: Graph-based representations in pattern recognition
Exact bounds on the order of the maximum clique of a graph
Discrete Applied Mathematics
A Unifying Framework for Relational Structure Matching
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
Quartic Formulation of Standard Quadratic Optimization Problems
Journal of Global Optimization
Replicator Equations, Maximal Cliques, and Graph Isomorphism
Neural Computation
Payoff-Monotonic Game Dynamics and the Maximum Clique Problem
Neural Computation
Multi-object image retrieval based on shape and topology
Image Communication
On the on-line rent-or-buy problem in probabilistic environments
Journal of Global Optimization
A convergent decomposition algorithm for support vector machines
Computational Optimization and Applications
A game-theoretic approach to partial clique enumeration
Image and Vision Computing
Computing Nash equilibria gets harder: new results show hardness even for parameterized complexity
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Graph-based quadratic optimization: A fast evolutionary approach
Computer Vision and Image Understanding
Review: Measuring instance difficulty for combinatorial optimization problems
Computers and Operations Research
An improved algorithm to test copositivity
Journal of Global Optimization
Journal of Global Optimization
On characterization of maximal independent sets via quadratic optimization
Journal of Heuristics
A continuous characterization of the maximum-edge biclique problem
Journal of Global Optimization
| Hi-index | 0.00 |
As is well known, the problem of finding a maximum clique in a graph isNP-hard. Nevertheless, NP-hard problems may have easy instances. This paperproposes a new, global optimization algorithm which tries to exploit favourabledata constellations, focussing on the continuous problem formulation: maximizea quadratic form over the standard simplex. Some general connections of thelatter problem with dynamic principles of evolutionary game theory areestablished. As an immediate consequence, one obtains a procedure whichconsists (a) of an iterative part similar to interior-path methods based on theso-called replicator dynamics; and (b) a routine to escape from inefficient,locally optimal solutions. For the special case of finding a maximum clique ina graph where the quadratic form arises from a regularization of the adjacencematrix, part (b), i.e. escaping from maximal cliques not of maximal size, isaccomplished with block pivoting methods based on (large) independent sets,i.e. cliques of the complementary graph. A simulation study is included whichindicates that the resulting procedure indeed has some merits.