# Approximability

## Approximation Algorithms for Facial Cycles in Planar Embeddings

Consider the following combinatorial problem$:$ Given a planar graph $G$ and a set of simple cycles $\mathcal C$ in $G$, find a planar embedding $\mathcal E$ of $G$ such that the number of cycles in $\mathcal C$ that bound a face in $\mathcal E$ is …

## Planar Graphs with Vertices in Prescribed Regions: models, algorithms, and complexity

The volume and the complexity of structured relational information created and handled by modern information systems has drastically increased. More and more often, data are generated so quickly that they cannon even be completely displayed or …

## Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that …