Combinatorica
The time complexity of maximum matching by simulated annealing
Journal of the ACM (JACM)
Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Towards an analysis of local optimization algorithms
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Go with the winners for graph bisection
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for Graph Partitioning on the Planted Partition Model
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Topics in black-box combinatorial optimization
Topics in black-box combinatorial optimization
Empirical and analytic approaches to understanding local search heuristics
Empirical and analytic approaches to understanding local search heuristics
Optimization by iterative improvement: an experimental evaluation on two-way partitioning
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Improved Algorithms for the Random Cluster Graph Model
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Hill-Climbing vs. Simulated Annealing for Planted Bisection Problems
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Max Cut for Random Graphs with a Planted Partition
Combinatorics, Probability and Computing
A spectral heuristic for bisecting random graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A rigorous analysis of population stratification with limited data
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Single- and multi-objective evolutionary algorithms for graph bisectioning
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
A comparison of simulated annealing with a simple evolutionary algorithm
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
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We analyze the behavior of hill-climbing algorithms for the minimum bisection problem on instances drawn from the “planted bisection” random graph model, Gn,p,q, previously studied in [3, 4, 10, 11, 14, 9, 7]. This is one of the few problem distributions for which various popular heuristic methods, such as simulated annealing, have been proven to succeed. However, it has been open whether these sophisticated methods were necessary, or whether simpler heuristics would also work. Juels [14] made the first progress towards an answer by showing that simple hill-climbing does suffice for very wide separations between p and q.Here we give a more complete answer. A simple, polynomial-time, hill-climbing algorithm for this problem is given and shown to succeed in finding the planted bisection with high probability if p - q = &OHgr; (n-½ln3n). For dense graphs, this matches the condition for optimality of the planted bisection to within a polylogarithmic factor. Furthermore, we show that a generic randomized hill-climbing algorithm succeeds in finding the planted bisection in polynomial time if p - q = &OHgr; (n-¼ ln3 n), for any ∈ 0. This algorithm, studied also by [14], is a degenerate case of both Metropolis and go-with-the-winners, and the range here properly includes those analyzed in [11, 9, 14]. So this result implies, extends, and unifies those from [11, 9, 14]. Thus, to get a provable distinction between simulated annealing and hill-climbing for natural problems will require considerable progress both on new positive results for SA and new negative results for hill-climbing methods.