Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Finding a large hidden clique in a random graph
proceedings of the eighth international conference on Random structures and algorithms
A spectral technique for random satisfiable 3CNF formulas
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Coloring Bipartite Hypergraphs
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A spectral heuristic for bisecting random graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Spectral techniques applied to sparse random graphs
Random Structures & Algorithms
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Spectral clustering by recursive partitioning
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
On the Security of Goldreich's One-Way Function
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A spectral method for MAX2SAT in the planted solution model
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Separating populations with wide data: a spectral analysis
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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We study random instances of a general graph partitioning problem: the vertex set of the random input graph G consists of k classes V1,...,Vk, and Vi-Vj-edges are present with probabilities pij independently. The main result is that with high probability a partition S1,...,Sk of G that coincides with V1,...,Vk on a huge subgraph core(G) can be computed in polynomial time via spectral techniques. The result covers the case of sparse graphs (average degree O(1)) as well as the massive case (average degree #V(G)–O(1)). Furthermore, the spectral algorithm is adaptive in the sense that it does not require any information about the desired partition beyond the number k of classes.