In the first reporting period, a particular focus
have been basic operations on very large graphs.
Graphs model relations (edges) between objects
(nodes) and are thus a universal modelling tool
for computer science. For example, graphs
model such diverse things as road networks, social
networks, discretized models in numerical
simulations, (real and artifical) neural networks,
or control flow in computer programs. For example, we investigated
the minimum spanning tree problem where we look
for the minimum cost selection of edges that
connect all nodes. Our algorithm scales to many
thousands of processing cores and trillions of
edges, with performance and scalability
several orders of magnitude better than the
previous state-of-the-art. Similarly, a case study
in graph analysis considered the fundamental task
of finding triangles which are indicative of
densely connected parts of the graph. This
problem requires communication and
computation that grows faster than the network
size. Nevertheless, the designed code is able to
process huge graphs in reasonable time even if
they only fit into the joined memory of many
thousands of processors.
Another success story is our Mallob SAT solver.
SAT solving is about deciding whether a formula in
propositional logic is satisfiable, i.e. whether
it has an assignment of truth values to logical variables
that makes the formula true. This is a
prototypical hard computational problem that
underlies many applications such as hardware and
software verification, automatic theorem proving,
cryptographical problems, etc. Mallob is able to
effecively coordinate hundreds to thousands of
sequential SAT solvers to jointly solve complex
SAT problems. It does so by effectively sharing
learned information (clauses) between the
individual solvers. Another factor of
parallelization is achieved by flexibly assigning
computing resources to multiple streams of problem
instances. Mallob, is malleable, i.e. within
milliseconds it can adapt the amount of used
resources based on the difficulty of the input and
the available processing power. In contrast,
traditional supercomputers manage their resources
on the time scale of hours which would be useless
for SAT solving where it is difficult to see
whether a problems requires seconds or weeks of
computation.
A crucial tool for storing and processing large
data sets are data compression techniques that
allow processing the data without uncompressing
it. We obtained several surprising results in this
direction by showing that theoretical lower bounds
on space consumption can actually be approached by
practical solutions. This includes a dictionary
data structure that can store a set of compressed
objects with virtually no space overhead for
making it searchable. Another such component are
perfect hash function that assign unique yet
compact identifiers to objects. This functionality
helps to improve data bases and various
applications, e.g. in bioinformatics.
