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Subgraph sparsification and nearly optimal ultrasparsifiers
Proceedings of the forty-second ACM symposium on Theory of computing
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INFOCOM'10 Proceedings of the 29th conference on Information communications
Tree embeddings for two-edge-connected network design
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Spanners of bounded degree graphs
Information Processing Letters
A Tight Upper Bound on the Probabilistic Embedding of Series-Parallel Graphs
SIAM Journal on Discrete Mathematics
Near linear-work parallel SDD solvers, low-diameter decomposition, and low-stretch subgraphs
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
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TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Using petal-decompositions to build a low stretch spanning tree
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Algorithms, graph theory, and the solution of laplacian linear equations
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Approximation algorithms and hardness results for shortest path based graph orientations
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Parallel graph decompositions using random shifts
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$ over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T \sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. Our result is obtained via a new approach of building ``highways'' between portals and a new strong diameter probabilistic decomposition theorem.