Parallel 'Go with the Winners' Algorithms in the LogP Model
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
Automated Design of Quantum Circuits
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Randomized Shared Queues Applied to Distributed Optimization Algorithms
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Go with the Winners Algorithms for Cliques in Random Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Comparing evolutionary algorithms to the (1+1) -EA
Theoretical Computer Science
Stochastic simulation algorithms for dynamic probabilistic networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Algorithm portfolio design: theory vs. practice
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Multi-objective go with the winners algorithm: a preliminary study
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Sensitivity-guided metaheuristics for accurate discrete gate sizing
Proceedings of the International Conference on Computer-Aided Design
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We can view certain randomized optimization algorithms as rules for randomly moving a particle around in a state space; each state might correspond to a distinct solution to the optimization problem, or more generally, the state space might express some other structure underlying the optimization algorithm. In this setting, a general paradigm for designing heuristics is to run several simulations of the algorithm simultaneously, and every so often classify the particles as "doing well" or "doing badly", and move each particle that is "doing badly" to the position of one that is "doing well". In this paper, we give a rigorous analysis of such a "go with the winners" scheme in the concrete setting of searching for a deep leaf in a tree. There are two relevant parameters of the tree: its depth d, and another parameter /spl kappa/ which is a measure of the imbalance of the tree. We prove that the running time of the "go with the winners" scheme (to achieve 99% probability of success) is bounded by a polynomial in d and /spl kappa/. By contrast, the simple restart scheme: run several independent simulations and pick the deepest leaf encountered takes time exponential in /spl kappa/ and d in the worst-case. We also show that any algorithm that guarantees a constant probability of success must have worst case running time at least /spl kappa/d.