19 citations · 36 across the 15 of their papers we have counts for
6 papers · 1 filter
A threshold for online balancing of sparse i.i.d. vectors
Dylan J. Altschuler, Konstantin Tikhomirov
Consider the task of \textit{online} vector balancing for stochastic arrivals , where the time horizon satisfies , and the are i.i.d uniform -…
Metric Poincaré inequalities for graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
This article obtains purely metric counterparts of cornerstone results in the theory of embedding graphs into normed spaces. Our first main result is a metric analogue of Matoušek'…
Metric dimension reduction modulus for superlogarithmic distortion
Dylan J. Altschuler, Konstantin Tikhomirov
The metric dimension reduction modulus is the smallest such that every --point metric space can be embedded into some -dimensional normed space, with…
Discrete Poincaré inequalities and universal approximators for random graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
Nonlinear Poincaré inequalities are indispensable tools in the study of dimension reduction and low-distortion embeddings of graphs into metric spaces, and have found remarkable al…
A universal threshold for geometric embeddings of trees
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
A graph is geometrically embeddable into a normed space when there is a mapping such that if and only if , for…
Universal geometric non-embedding of random regular graphs
Dylan J. Altschuler, Konstantin Tikhomirov
Let be fixed, be a large integer. It is a classical result that --regular expanders on vertices are not embeddable as geometric (distance) graphs into E…