Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An approximation algorithm for the covering Steiner problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Lectures on Discrete Geometry
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Embeddings of finite metrics
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
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The subject of graph embeddings deals with embedding a finite point set in a given metric space by points in another target metric space in such a way that distances in the new space are at least, but not too much more, than distances in the old space. The largest new distance to old distance ratio over all pairs of points is called the distortion of the embedding. In this paper, we will study the distortion dist(G,H) while embedding metrics supported on a given graph G into metrics supported on a graph H of lower characteristic, where the characteristic 驴(H) of a graph H is the quantity E - V + 1 (E is the number of edges and V is the number of vertices in H). We will prove the following lower bounds for such embeddings which generalize and improve lower bounds given in [10]. - If |G| = |H| and 驴(G) - 驴(H) = k, dist(G,H) 驴 gk - 1 - If 驴(G) - 驴(H) = k, dist(G,H) 驴 gk - 4/3.Further, we will also give an alternative proof for lower bounding the distortion when probabilistically embedding expander graphs into tree metrics. In addition, we also generalize this lower bound to the case when expander graphs probabilistically embed into graphs of constant characteristic.