Thomas Bläsius
Karlsruhe Institute of Technology
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Thomas Bläsius.
ACM Transactions on Algorithms | 2016
Thomas Bläsius; Ignaz Rutter
In this article, we define and study the new problem of S<scp>imultaneous</scp> PQ-O<scp>rdering</scp>. Its input consists of a set of PQ-trees, which represent sets of circular orders of their leaves, together with a set of child-parent relations between these PQ-trees, such that the leaves of the child form a subset of the leaves of the parent. S<scp>imultaneous</scp> PQ-O<scp>rdering</scp> asks whether orders of the leaves of each of the trees can be chosen <i>simultaneously</i>; that is, for every child-parent relation, the order chosen for the parent is an extension of the order chosen for the child. We show that S<scp>imultaneous</scp> PQ-O<scp>rdering</scp> is <i>NP</i>-complete in general, and we identify a family of instances that can be solved efficiently, the <i>2-fixed instances</i>. We show that this result serves as a framework for several other problems that can be formulated as instances of S<scp>imultaneous</scp> PQ-O<scp>rdering</scp>. In particular, we give linear-time algorithms for recognizing simultaneous interval graphs and extending partial interval representations. Moreover, we obtain a linear-time algorithm for P<scp>artially</scp> PQ-C<scp>onstrained</scp> P<scp>lanarity</scp> for biconnected graphs, which asks for a planar embedding in the presence of PQ-trees that restrict the possible orderings of edges around vertices, and a quadratic-time algorithm for S<scp>imultaneous</scp> E<scp>mbedding with</scp> F<scp>ixed</scp> E<scp>dges</scp> for biconnected graphs with a connected intersection. Both results can be extended to the case where the input graphs are not necessarily biconnected but have the property that each cutvertex is contained in at most two nontrivial blocks. This includes, for example, the case where both graphs have a maximum degree of 5.
graph drawing | 2013
Therese C. Biedl; Thomas Bläsius; Benjamin Niedermann; Martin Nöllenburg; Roman Prutkin; Ignaz Rutter
We present a simple and versatile formulation of grid-based graph representation problems as an integer linear program ILP and a corresponding SAT instance. In a grid-based representation vertices and edges correspond to axis-parallel boxes on an underlying integer grid; boxes can be further constrained in their shapes and interactions by additional problem-specific constraints. We describe a general d-dimensional model for grid representation problems. This model can be used to solve a variety of NP-hard graph problems, including pathwidth, bandwidth, optimum st-orientation, area-minimal bar-k visibility representation, boxicity-k graphs and others. We implemented SAT-models for all of the above problems and evaluated them on the Rome graphs collection. The experiments show that our model successfully solves NP-hard problems within few minutes on small to medium-size Rome graphs.
graph drawing | 2013
Thomas Bläsius; Annette Karrer; Ignaz Rutter
A simultaneous embedding of two graphs
ACM Transactions on Algorithms | 2016
Thomas Bläsius; Ignaz Rutter; Dorothea Wagner
G^{\mbox{\textcircled{1}}}
graph drawing | 2012
Thomas Bläsius; Ignaz Rutter
and
european symposium on algorithms | 2014
Thomas Bläsius; Guido Brückner; Ignaz Rutter
G^{\mbox{\textcircled{2}}}
international symposium on parameterized and exact computation | 2017
Thomas Bläsius; Tobias Friedrich; Martin Schirneck
with common graph
Theoretical Computer Science | 2016
Thomas Bläsius; Ignaz Rutter
G=G^{\mbox{\textcircled{1}}} \cap G^{\mbox{\textcircled{2}}}
graph drawing | 2014
Thomas Bläsius; Ignaz Rutter
is a pair of planar drawings of
international conference on algorithms and complexity | 2015
Thomas Bläsius; Sebastian Lehmann; Ignaz Rutter
G^{\mbox{\textcircled{1}}}