Given a triangulated planar graph G on n vertices and an integer r< n, an r--division of G with
few holes is a decomposition of G into O (n/r) regions of size at most r such that each region …

We consider a scenario in which a data owner outsources storage of a large graph to an
untrusted server; the server performs computations on this graph in response to queries from …

We prove a geometric version of the graph separator theorem for the unit disk intersection
graph: for any set of n unit disks in the plane there exists a line ℓ such that ℓ intersects at …

Route planning in transportation networks is a fundamental problem with numerous
interesting applications. Probably one of the best known applications are navigation devices …

We consider a scenario in which a data owner outsources storage of a large graph to an
untrusted server; the server performs computations on this graph in response to queries from …

Graphs and networks play a relevant role in modern science: graphs are clearly
fundamental in computer science and related fields (eg discrete mathematics) and they …

This chapter collects the fundamental background for the following three chapters as well as
an introduction to the problems we study in this thesis. Furthermore, an overview of the …

We investigate the practicality of approximation schemes for optimization problems in planar
graphs based on balanced separators. The first polynomial-time approximation schemes …

In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder
woods where the number of incoming edges of each color at each vertex is balanced as …

Exact learning aims at unambiguously determining an unknown concept from answers to a
carefully crafted set of questions, where each answer, given by an all-knowing oracle …