Finding a large hidden clique in a random graph
proceedings of the eighth international conference on Random structures and 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 works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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
Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
Boosting spectral partitioning by sampling and iteration
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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A partitioning of a set of n items is a grouping of these items into k disjoint, equally sized classes. 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 a partition is given, which is obscured by random noise, i.e., edges within a class can get removed and edges between classes can get inserted. The task is to reconstruct the planted partition from this graph. In the model that we study the number k of classes controls the difficulty of the task. We design a spectral partitioning algorithm that asymptotically almost surely reconstructs up to $k = c\sqrt{n}$ partitions, where c is a small constant, in time Ck poly(n), where C is another constant.