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Dive into the research topics where Thomas Bläsius is active.

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Featured researches published by Thomas Bläsius.


ACM Transactions on Algorithms | 2016

Simultaneous PQ-Ordering with Applications to Constrained Embedding Problems

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

Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings

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

Simultaneous Embedding: Edge Orderings, Relative Positions, Cutvertices

Thomas Bläsius; Annette Karrer; Ignaz Rutter

A simultaneous embedding of two graphs


ACM Transactions on Algorithms | 2016

Optimal Orthogonal Graph Drawing with Convex Bend Costs

Thomas Bläsius; Ignaz Rutter; Dorothea Wagner

G^{\mbox{\textcircled{1}}}


graph drawing | 2012

Disconnectivity and relative positions in simultaneous embeddings

Thomas Bläsius; Ignaz Rutter

and


european symposium on algorithms | 2014

Complexity of Higher-Degree Orthogonal Graph Embedding in the Kandinsky Model

Thomas Bläsius; Guido Brückner; Ignaz Rutter

G^{\mbox{\textcircled{2}}}


international symposium on parameterized and exact computation | 2017

The Parameterized Complexity of Dependency Detection in Relational Databases

Thomas Bläsius; Tobias Friedrich; Martin Schirneck

with common graph


Theoretical Computer Science | 2016

A new perspective on clustered planarity as a combinatorial embedding problem

Thomas Bläsius; Ignaz Rutter

G=G^{\mbox{\textcircled{1}}} \cap G^{\mbox{\textcircled{2}}}


graph drawing | 2014

A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem

Thomas Bläsius; Ignaz Rutter

is a pair of planar drawings of


international conference on algorithms and complexity | 2015

Orthogonal Graph Drawing with Inflexible Edges

Thomas Bläsius; Sebastian Lehmann; Ignaz Rutter

G^{\mbox{\textcircled{1}}}

Collaboration


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Ignaz Rutter

Karlsruhe Institute of Technology

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Anton Krohmer

Hasso Plattner Institute

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Dorothea Wagner

Karlsruhe Institute of Technology

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Andreas Gemsa

Karlsruhe Institute of Technology

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Franziska Wegner

Karlsruhe Institute of Technology

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Moritz Baum

Karlsruhe Institute of Technology

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Benjamin Niedermann

Karlsruhe Institute of Technology

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