Approximate max-flow min-(multi)cut theorems and their applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Coloring random and semi-random k-colorable graphs
Journal of Algorithms
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Finding a large hidden clique in a random graph
proceedings of the eighth international conference on Random structures and algorithms
Go with the winners for graph bisection
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Finding and certifying a large hidden clique in a semirandom graph
Random Structures & Algorithms
Towards adaptive Web sites: conceptual framework and case study
Artificial Intelligence - Special issue on Intelligent internet systems
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth 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
Heuristics for semirandom graph problems
Journal of Computer and System Sciences
Algorithms for Graph Partitioning on the Planted Partition Model
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A spectral heuristic for bisecting random graphs
Random Structures & Algorithms
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fast solution of some random NP-hard problems
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Simulated annealing for graph bisection
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Approximate clustering without the approximation
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
How to play unique games on expanders
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Min-max Graph Partitioning and Small Set Expansion
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Sorting noisy data with partial information
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real-world instances. The model is more flexible than the semi-random model of Feige and Kilian and planted random model of Bui, Chaudhuri, Leighton and Sipser. We develop a general framework for solving semi-random instances and apply it to several problems of interest. We present constant factor bi-criteria approximation algorithms for semi-random instances of the Balanced Cut, Multicut, Min Uncut, Sparsest Cut and Small Set Expansion problems. We also show how to almost recover the optimal solution if the instance satisfies an additional expanding condition. Our algorithms work in a wider range of parameters than most algorithms for previously studied random and semi-random models. Additionally, we study a new planted algebraic expander model and develop constant factor bi-criteria approximation algorithms for graph partitioning problems in this model.