IT-Nachwuchsforschung in Österreich

1 Dwork, C., Kenthapadi, K., McSherry, F., Mironov, I., & Naor, M. (2006a). Our data, ourselves:
Privacy via distributed noise generation. In Advances in Cryptology–EUROCRYPT..
2 badi, M., Chu, A., Goodfellow, I., McMahan, H.B., Mironov, I., Talwar, K., Zhang, L., 2016.
Deep Learning with Differential Privacy, in: Proceedings of the 2016 ACM SIGSAC Conference
on Computer and Communications Security
3 Anastasia Pustozerova, Jan Baumbach, and Rudolf Mayer. Differentially Private Federated
Learning: Privacy and Utility Analysis of Output Perturbation and DP-SGD. In 2023
IEEE International Conference on Big Data (Big Data)
Anastasia
Pustozerova
ist Machine Learning
Researcher
bei SBA Research
und der Universität
Wien. Ihre Forschungsinteressen sind
Privacy-Preserving Machine Learning,
Federated Learning und Differential
Privacy.
Distributed Computing and Dynamic Graph Algorithms
von Tijn de Vos
Matrix-Vector Multiplication
in Distributed Models
Part of theoretical computer science
is to develop new algorithms with provable
guarantees on their running time.
One substantial subfield consists of
graph algorithms. Graphs model several
real-world networks such as road networks
or social networks. The goal is to
efficiently compute properties of graphs
such as finding the distance between
two points in a transportation network
(the shortest path problem) or finding
well-connected nodes in a social network
(community detection).
CONTINUOUS OPTIMIZATION
Graphs are discrete objects and problems
are often solved with combinatorial, discrete
algorithms. In another part of computer
science, we have continuous optimization,
a branch of optimization where
the variables can take continuous values.
This is opposed to discrete optimization,
where they can only take discrete values.
Surprisingly, in 2004 Spielman and Teng
showed in their seminal work, that led
them to winning the Gödel prize, that discrete
graph problems can benefit from
continuous optimization techniques.
Examples of discrete problems that
benefit from continuous optimization
techniques include computing shortest
paths or computing the maximum flow.
In the latter, the goal is to send the maximum
amount of flow from a source
to a target through the network. Such
algorithms have been developed in the
normal, ‘central’ model of computation
in the last 20 years. Recently, it led to the
celebrated near-linear time algorithm for
maximum flow.
A first example of optimization
techniques is solving a system of equations.
When these equations relate to the
structure of a graph, we call it a Laplacian
system. With continuous optimization,
the goal is to solve this (much) faster than
just trying possible values. A more involved
example is solving linear programs:
optimizing an objective function under a
set of linear constraints. This generalizes
problems like shortest paths, maximum
matching, and maximum flow.
MATRIX-VECTOR MULTIPLICATI-
ON
It turns out that one of the most important
primitives for solving optimization
problems is matrix-vector multiplication.
Where matrix multiplication is an (in)fa-
26 OCG Journal | 01 • 2024