2 citations · 4 across the 5 of their papers we have counts for
5 papers
A lower bound on dimension reduction for trees in \ell_1
James R. Lee, Mohammad Moharrami
There is a constant c > 0 such that for every and , the following holds. Any mapping from the -point star metric into with bi-Lipschitz dis…
A node-capacitated Okamura-Seymour theorem
James R. Lee, Manor Mendel, Mohammad Moharrami
The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists…
On the Hausdorff dimension of ultrametric subsets in R^n
James R. Lee, Manor Mendel, Mohammad Moharrami
For every e>0, any subset of R^n with Hausdorff dimension larger than (1-e)n must have ultrametric distortion larger than 1/(4e).
Dimension reduction for finite trees in L_1
James R. Lee, Arnaud de Mesmay, Mohammad Moharrami
We show that every n-point tree metric admits a (1+eps)-embedding into a C(eps) log n-dimensional L_1 space, for every eps > 0, where C(eps) = O((1/eps)^4 log(1/eps)). This matches…
On the optimality of gluing over scales
Alexander Jaffe, James R. Lee, Mohammad Moharrami
We show that for every , there exist -point metric spaces (X,d) where every "scale" admits a Euclidean embedding with distortion at most , but the whole space requires…