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On the second eigenvalue of random regular graphs
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Lower bounds for the partitioning of graphs
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Edge-Bisection of Chordal Rings
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Improved Algorithms for the Random Cluster Graph Model
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ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
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
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Spectral clustering by recursive partitioning
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Foundations and Trends® in Theoretical Computer Science
Graph partitioning via adaptive spectral techniques
Combinatorics, Probability and Computing
An efficient and accurate graph-based approach to detect population substructure
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Autonomous dynamic reconfiguration in multi-agent systems: improving the quality and efficiency of collaborative problem solving
Correlation clustering with noisy input
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
An Efficient Sparse Regularity Concept
SIAM Journal on Discrete Mathematics
An adaptive spectral heuristic for partitioning random graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
A simple message passing algorithm for graph partitioning problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Approximation algorithms for semi-random partitioning problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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Fundamenta Informaticae
Sorting noisy data with partial information
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Graph Bisection is the problem of partitioning the vertices of a graph into two equal-size pieces so as to minimize the number of edges between the two pieces. This paper presents an algorithm that will, for almost all graphs in a certain class, output the minimum-size bisection. Furthermore the algorithm will yield, for almost all such graphs, a proof that the bisection is optimal. The algorithm is based on computing eigenvalues and eigenvectors of matrices associated with the graph.