Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Sparsest cuts and bottlenecks in graphs
Discrete Applied Mathematics - Computational combinatiorics
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
On weighted vs unweighted versions of combinatorial optimizationproblems
Information and Computation
Some optimal inapproximability results
Journal of the ACM (JACM)
NC-Algorithms for Graphs with Small Treewidth
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
On average distortion of embedding metrics into the line and into L1
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Cuts, Trees and ℓ1-Embeddings of Graphs*
Combinatorica
On the impossibility of dimension reduction in l1
Journal of the ACM (JACM)
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Embedding k-Outerplanar Graphs into l1
SIAM Journal on Discrete Mathematics
ON THE HARDNESS OF APPROXIMATING MULTICUT AND SPARSEST-CUT
Computational Complexity
Lp metrics on the Heisenberg group and the Goemans-Linial conjecture
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Embeddings of Topological Graphs: Lossy Invariants, Linearization, and 2-Sums
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Polynomial flow-cut gaps and hardness of directed cut problems
Journal of the ACM (JACM)
On the geometry of graphs with a forbidden minor
Proceedings of the forty-first annual ACM symposium on Theory of computing
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Robust Algorithms for on Minor-Free Graphs Based on the Sherali-Adams Hierarchy
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Improved Lower Bounds for Embeddings into $L_1$
SIAM Journal on Computing
Approximation Algorithms for Treewidth
Algorithmica
Coarse Differentiation and Multi-flows in Planar Graphs
Discrete & Computational Geometry
A $(\log n)^{\Omega(1)}$ Integrality Gap for the Sparsest Cut SDP
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
SDP Integrality Gaps with Local ell_1-Embeddability
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Flow-cut gaps for integer and fractional multiflows
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Near-optimal distortion bounds for embedding doubling spaces into L1
Proceedings of the forty-third annual ACM symposium on Theory of computing
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
Tree-width and the Sherali-Adams operator
Discrete Optimization
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We give a 2-approximation algorithm for the non-uniform Sparsest Cut problem that runs in time nO(k), where k is the treewidth of the graph. This improves on the previous 22k-approximation in time poly(n) 2O(k) due to Chlamtac et al. [18]. To complement this algorithm, we show the following hardness results: If the non-uniform Sparsest Cut has a ρ-approximation for series-parallel graphs (where ρ ≥ 1), then the MaxCut problem has an algorithm with approximation factor arbitrarily close to 1/ρ. Hence, even for such restricted graphs (which have treewidth 2), the Sparsest Cut problem is NP-hard to approximate better than 17/16 - ε for ε 0; assuming the Unique Games Conjecture the hardness becomes 1/αGW - ε. For graphs with large (but constant) treewidth, we show a hardness result of 2 - ε assuming the Unique Games Conjecture. Our algorithm rounds a linear program based on (a subset of) the Sherali-Adams lift of the standard Sparsest Cut LP. We show that even for treewidth-2 graphs, the LP has an integrality gap close to 2 even after polynomially many rounds of Sherali-Adams. Hence our approach cannot be improved even on such restricted graphs without using a stronger relaxation.