Combinatorica
Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
SIAM Journal on Matrix Analysis and Applications
Combinatorial properties and complexity of a max-cut approximation
European Journal of Combinatorics
Laplacian eigenvalues and the maximum cut problem
Mathematical Programming: Series A and B
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Bipartite Subgraphs and the Smallest Eigenvalue
Combinatorics, Probability and Computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximating the Cut-Norm via Grothendieck's Inequality
SIAM Journal on Computing
Graph partitioning using single commodity flows
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
SDP gaps and UGC-hardness for MAXCUTGAIN
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Lifts, Discrepancy and Nearly Optimal Spectral Gap
Combinatorica
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An optimal sdp algorithm for max-cut, and equally optimal long code tests
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On partitioning graphs via single commodity flows
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximations for the isoperimetric and spectral profile of graphs and related parameters
Proceedings of the forty-second ACM symposium on Theory of computing
Fast SDP algorithms for constraint satisfaction problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating Semidefinite Packing Programs
SIAM Journal on Optimization
Maximizing Non-monotone Submodular Functions
SIAM Journal on Computing
On quadratic programming with a ratio objective
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Quantitative measurement and method for detecting anti-community structures in complex networks
International Journal of Wireless and Mobile Computing
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We describe a new approximation algorithm for Max Cut. Our algorithm runs in ~O(n2) time, where n is the number of vertices, and achieves an approximation ratio of .531. On instances in which an optimal solution cuts a 1-ε fraction of edges, our algorithm finds a solution that cuts a 1-4√ε + 8ε-o(1) fraction of edges. Our main result is a variant of spectral partitioning, which can be implemented in nearly linear time. Given a graph in which the Max Cut optimum is a 1-ε fraction of edges, our spectral partitioning algorithm finds a set S of vertices and a bipartition L,R=S-L of S such that at least a 1-O(√ε) fraction of the edges incident on S have one endpoint in L and one endpoint in R. (This can be seen as an analog of Cheeger's inequality for the smallest eigenvalue of the adjacency matrix of a graph.) Iterating this procedure yields the approximation results stated above. A different, more complicated, variant of spectral partitioning leads to a polynomial time algorithm that cuts a 1/2 + e-Ω(1/ε) fraction of edges in graphs in which the optimum is 1/2 + ε.