Algorithmic theory of random graphs
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Algorithms for graph partitioning on the planted partition model
Random Structures & Algorithms
Improved Algorithms for the Random Cluster Graph Model
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Max Cut for Random Graphs with a Planted Partition
Combinatorics, Probability and Computing
Spectral norm of random matrices
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Bounding the misclassification error in spectral partitioning in the planted partition model
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Reconstructing many partitions using spectral techniques
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
| Hi-index | 0.00 |
A partition of a set of n items is a grouping of the items into k disjoint classes of equal size. Any partition can be modeled as a graph: the items become the vertices of the graph and two vertices are connected by an edge if and only if the associated items belong to the same class. In a planted partition model a graph that models the planted partition is obscured by random noise, i.e., edges within a class can get removed and edges between classes can get inserted at random. We study the task to reconstruct the planted partition from this graph whose complexity can be controlled by the number k of classes if the noise level is fixed. The best bounds on k where the classes can be reconstructed correctly almost surely are achieved by spectral algorithms. We show that a combination of random sampling and iterating the spectral approach can boost its performance in the sense that the number of classes that can be reconstructed correctly asymptotically almost surely can be as large as $k = c\sqrt{n}/{\rm loglog}n$ for some constant c. This extends the range of k for which such guarantees can be given for any efficient algorithm.