Data-driven approaches have been applied to reduce the cost of accurate computational studies on materials, by using only a small number of expensive reference electronic structure calculations for a representative subset of the materials space, and using ...
In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...
An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius ρ such that there exist balls of radius ρ around ...
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metr ...
Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and proso ...
We study the k-server problem in the resource augmentation setting, i.e., when the performance of the online algorithm with k servers is compared to the offline optimal solution with h
An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius rho such that there exist balls of radius rho aro ...
Let R be a finite set of terminals in a convex metric space (M, d). We give approximation algorithms for problems of finding a minimum size set S subset of M of additional points such that the unit-disc graph G[R boolean OR S] of R boolean OR S satisfies s ...
In this paper, we study multidimensional persistence modules (Carlsson and Zomorodian in Discrete Comput Geom 42(1):71-93, 2009; Lesnick in Found Comput Math 15(3):613-650, 2015) via what we call tame functors and noise systems. A noise system leads to a p ...
