Combinatorica
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the optimality of the random hyperplane rounding technique for max cut
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Understanding Parallel Repetition Requires Understanding Foams
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
A Linear Round Lower Bound for Lovasz-Schrijver SDP Relaxations of Vertex Cover
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Parallel repetition in projection games and a concentration bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of 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
A Counterexample to Strong Parallel Repetition
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Rounding Parallel Repetitions of Unique Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximations for the isoperimetric and spectral profile of graphs and related parameters
Proceedings of the forty-second 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
Improved rounding for parallel repeated unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Computational complexity and information asymmetry in election audits with low-entropy randomness
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
Algorithmic extensions of cheeger's inequality to higher eigenvalues and partitions
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
Approximating CSPs with global cardinality constraints using SDP hierarchies
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Hypercontractivity, sum-of-squares proofs, and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Multi-way spectral partitioning and higher-order cheeger inequalities
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Many sparse cuts via higher eigenvalues
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of 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
Lower bounds for treewidth of product graphs
Discrete Applied Mathematics
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The edge expansion of a subset of vertices S ⊆ V in a graph G measures the fraction of edges that leave S. In a d-regular graph, the edge expansion/conductance Φ(S) of a subset S ⊆ V is defined as Φ(S) = (|E(S, V\S)|)/(d|S|). Approximating the conductance of small linear sized sets (size δ n) is a natural optimization question that is a variant of the well-studied Sparsest Cut problem. However, there are no known algorithms to even distinguish between almost complete edge expansion (Φ(S) = 1-ε), and close to 0 expansion. In this work, we investigate the connection between Graph Expansion and the Unique Games Conjecture. Specifically, we show the following: We show that a simple decision version of the problem of approximating small set expansion reduces to Unique Games. Thus if approximating edge expansion of small sets is hard, then Unique Games is hard. Alternatively, a refutation of the UGC will yield better algorithms to approximate edge expansion in graphs. This is the first non-trivial "reverse" reduction from a natural optimization problem to Unique Games. Under a slightly stronger UGC that assumes mild expansion of small sets, we show that it is UG-hard to approximate small set expansion. On instances with sufficiently good expansion of small sets, we show that Unique Games is easy by extending the techniques of [4].