Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A polynomial time approximation scheme for minimum routing cost spanning trees
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Deterministic Polylog Approximation for Minimum Communication Spanning Trees
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Using petal-decompositions to build a low stretch spanning tree
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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In [6] it is shown that every graph can be probabilistically embedded into a distribution over its spanning trees with expected distortion O(log2 n log log n), narrowing the gap left by [1], where a lower bound of Ω(log n) is established. This lower bound holds even for the class of series-parallel graphs as proved in [8]. In this paper we close this gap for series-parallel graphs, namely we prove that every n-vertex series-parallel graph can be probabilistically embedded into a distribution over its spanning trees with expected stretch O(log n) for every two vertices. We gain our upper bound by presenting a polynomial time probabilistic algorithm that constructs spanning trees with low expected stretch. This probabilistic algorithm can be derandomized to yield a deterministic polynomial time algorithm for constructing a spanning tree of a given series-parallel graph G, whose communication cost is at most O(log n) times larger than that of G.