Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Approximating clique is almost NP-complete (preliminary version)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Polyhedral combinatorics and neural networks
Neural Computation
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
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
The Dynamics of Nonlinear Relaxation Labeling Processes
Journal of Mathematical Imaging and Vision
Evolution towards the Maximum Clique
Journal of Global Optimization
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Exact bounds on the order of the maximum clique of a graph
Discrete Applied Mathematics
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Branch-and-bound approaches to standard quadratic optimization problems
Journal of Global Optimization
Ellipsoidal Approach to Box-Constrained Quadratic Problems
Journal of Global Optimization
An effective local search for the maximum clique problem
Information Processing Letters
Replicator Equations, Maximal Cliques, and Graph Isomorphism
Neural Computation
Payoff-Monotonic Game Dynamics and the Maximum Clique Problem
Neural Computation
Approximating the maximum vertex/edge weighted clique using local search
Journal of Heuristics
A Continuous Characterization of Maximal Cliques in k-Uniform Hypergraphs
Learning and Intelligent Optimization
A game-theoretic approach to partial clique enumeration
Image and Vision Computing
An effective local search for the maximum clique problem
Information Processing Letters
Connected substructure similarity search
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
A complete resolution of the Keller maximum clique problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An improved algorithm to test copositivity
Journal of Global Optimization
Finding top-k similar graphs in graph databases
Proceedings of the 15th International Conference on Extending Database Technology
Breakout Local Search for maximum clique problems
Computers and Operations Research
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We propose a new heuristic for approximating the maximum clique problem based on a detailed analysis of a class of continuous optimization models which provide a complete characterization of solutions to this NP-hard combinatorial problem. We start from a known continuous formulation of the maximum clique, and tackle the search for local solutions with replicator dynamics, a class of dynamical systems developed in various branches of mathematical biology. Hereby, we add to the objective used in previous works a regularization term that controls the global shape of the energy landscape, that is the function actually maximized by the dynamics. The parameter controlling the regularization is changed during the evolution of the dynamical system to render inefficient local solutions (which formerly were stable) unstable, thus conducting the system to escape from sub-optimal points, and so to improve the final results. The role of this parameter is thus superficially similar to that of temperature in simulated annealing in the sense that its variation allows to find better solutions for the problem at hand. We demonstrate several theoretical results on the regularization term and we farther support the validity of this approach, reporting on its performances when applied to selected DIMACS benchmark graphs.