. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...
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 ...
In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...
The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...
Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...
Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. ...
In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices.In the first part, we consider algorithms for building ...
We consider a learning system based on the conventional multiplicative weight ( MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the sys ...
We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...
