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Structure Theory for Directed Graphs

Objective

Structural graph theory has proved to be a powerful tool for coping
with computational intractability. It provides a wealth of
concepts and results that can be used to design efficient algorithms for
hard computational problems on specific classes of graphs that
occur naturally in applications.

In many applications in computer science, the natural mathematical
model are directed graphs. Unfortunately, research in
structural graph theory has so far almost exclusively focussed on
undirected graphs and no structure theory for directed graphs
comparable to the tree-width and graph minors based approach for
undirected graphs has been developed that would provide for a similar
set of tools and concepts to deal with computational problems on
directed graphs.

The objective of this proposal is to develop such a structure
theory aimed specifically at algorithmic applications on directed
graphs. The novelty of our approach is that

a) it is based on directed minors which allows us to avoid
the algorithmic problems faced by existing digraph width
measures and has not been studied before in this context and

b) it facilitates our recent proof of the excluded directed
grid theorem which is likely to allow entirely new algorithmic
techniques for directed graphs.

The focus of the project is on the development of the structural
foundations and algorithmic techniques for designing efficient algorithms
for a wide range of algorithmic digraph problems. In particular, we
will use an approach based on logical definability for developing such
algorithmic techniques.

Furthermore, we will apply our methods to two specific application
areas, model-checking in computer-aided verification and inference
problems in Bayesian networks.

Call for proposal

ERC-2014-CoG
See other projects for this call

Host institution

TECHNISCHE UNIVERSITAT BERLIN
Address
Strasse Des 17 Juni 135
10623 Berlin
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 826 773

Beneficiaries (1)

TECHNISCHE UNIVERSITAT BERLIN
Germany
EU contribution
€ 1 826 773
Address
Strasse Des 17 Juni 135
10623 Berlin
Activity type
Higher or Secondary Education Establishments