473 research outputs found
Pitfalls of using PQ-trees in Automatic Graph Drawing
A number of erroneous attempts involving PQ-trees in the context of automatic graph drawing algorithms have been presented in the literature in recent years. In order to prevent future research from constructing algorithms with similar errors we point out some of the major mistakes. In particular, we examine erroneous usage of the PQ-tree data structure in algorithms for computing maximal planar subgraphs and an algorithm for testing leveled planarity of leveled directed acyclic graphs with several sources and sinks
Planarization With Fixed Subgraph Embedding
The visualization of metabolic networks using techniques of graph drawing has recently become an important research area. In order to ease the analysis of these networks, readable layouts are required in which certain known network components are easily recognizable. In general, the topology of the drawings produced by traditional graph drawing algorithms does not reflect the biologists' expert knowledge on particular substructures of the underlying network. To deal with this problem we present a constrained planarization method---an algorithm which computes a graph layout in the plane preserving the predefined shape for the specified substructures while minimizing the overall number of edge-crossings
Planarization With Fixed Subgraph Embedding
The visualization of metabolic networks using techniques of graph drawing has recently become an important research area. In order to ease the analysis of these networks, readable layouts are required in which certain known network components are easily recognizable. In general, the topology of the drawings produced by traditional graph drawing algorithms does not reflect the biologists' expert knowledge on particular substructures of the underlying network. To deal with this problem we present a constrained planarization method---an algorithm which computes a graph layout in the plane preserving the predefined shape for the specified substructures while minimizing the overall number of edge-crossings
Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity
We introduce and study the problem Ordered Level Planarity which asks for a
planar drawing of a graph such that vertices are placed at prescribed positions
in the plane and such that every edge is realized as a y-monotone curve. This
can be interpreted as a variant of Level Planarity in which the vertices on
each level appear in a prescribed total order. We establish a complexity
dichotomy with respect to both the maximum degree and the level-width, that is,
the maximum number of vertices that share a level. Our study of Ordered Level
Planarity is motivated by connections to several other graph drawing problems.
Geodesic Planarity asks for a planar drawing of a graph such that vertices
are placed at prescribed positions in the plane and such that every edge is
realized as a polygonal path composed of line segments with two adjacent
directions from a given set of directions symmetric with respect to the
origin. Our results on Ordered Level Planarity imply -hardness for any
with even if the given graph is a matching. Katz, Krug, Rutter and
Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where
contains precisely the horizontal and vertical directions, can be solved in
polynomial time [GD'09]. Our results imply that this is incorrect unless
. Our reduction extends to settle the complexity of the Bi-Monotonicity
problem, which was proposed by Fulek, Pelsmajer, Schaefer and
\v{S}tefankovi\v{c}.
Ordered Level Planarity turns out to be a special case of T-Level Planarity,
Clustered Level Planarity and Constrained Level Planarity. Thus, our results
strengthen previous hardness results. In particular, our reduction to Clustered
Level Planarity generates instances with only two non-trivial clusters. This
answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Kreisplanarität von Level-Graphen
In this dissertation we generalise the notion of level planar graphs in two directions: track planarity and radial planarity. Our main results are linear time algorithms both for the planarity test and for the computation of an embedding, and thus a drawing. Our algorithms use and generalise PQ-trees, which are a data structure for efficient planarity tests.In dieser Arbeit wird der Begriff Level-Planarität von Graphen auf zwei Arten erweitert: Spur-Planarität und radiale Level-Planarität. Die Hauptergebnisse sind Linearzeitalgorithmen zum Testen dieser Arten von Planarität und zur Erstellung einer entsprechenden Einbettung und somit einer Zeichnung. Die Algorithmen verwenden und generalisieren PQ-Bäume, eine bei effizienten Planaritätstests verwendete Datenstruktur
Scalable String and Suffix Sorting: Algorithms, Techniques, and Tools
This dissertation focuses on two fundamental sorting problems: string sorting
and suffix sorting. The first part considers parallel string sorting on
shared-memory multi-core machines, the second part external memory suffix
sorting using the induced sorting principle, and the third part distributed
external memory suffix sorting with a new distributed algorithmic big data
framework named Thrill.Comment: 396 pages, dissertation, Karlsruher Instituts f\"ur Technologie
(2018). arXiv admin note: text overlap with arXiv:1101.3448 by other author
Site Controller: A System for Computer-Aided Civil Engineering and Construction
A revolution\0\0\0 in earthmoving, a $100 billion industry, can be achieved with three components: the GPS location system, sensors and computers in bulldozers, and SITE CONTROLLER, a central computer system that maintains design data and directs operations. The first two components are widely available; I built SITE CONTROLLER to complete the triangle and describe it here. SITE CONTROLLER assists civil engineers in the design, estimation, and construction of earthworks, including hazardous waste site remediation. The core of SITE CONTROLLER is a site modelling system that represents existing and prospective terrain shapes, roads, hydrology, etc. Around this core are analysis, simulation, and vehicle control tools. Integrating these modules into one program enables civil engineers and contractors to use a single interface and database throughout the life of a project
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