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 all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

Improved Scalability By Using Hardware-Aware Thread Affinities

The complexity of an efficient thread management steadily rises with the number of processor cores and heterogeneities in the design of system architectures, e.g., the topologies of execution units and the memory architecture. In this paper, we show that using information about the system topology combined with a hardware-aware thread management is worthwhile. We present such a hardware-aware approach that utilizes thread affinity to automatically steer the mapping of threads to cores and experimentally analyze its performance. Our experiments show that we can achieve significantly better scalability and runtime stability compared to the ordinary dispatching of threads provided by the operating system

Improved Scalability By Using Hardware-Aware Thread Affinities

The complexity of an efficient thread management steadily rises with the number of processor cores and heterogeneities in the design of system architectures, e.g., the topologies of execution units and the memory architecture. In this paper, we show that using information about the system topology combined with a hardware-aware thread management is worthwhile. We present such a hardware-aware approach that utilizes thread affinity to automatically steer the mapping of threads to cores and experimentally analyze its performance. Our experiments show that we can achieve significantly better scalability and runtime stability compared to the ordinary dispatching of threads provided by the operating system

Straight-line Drawability of a Planar Graph Plus an Edge

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing

The Open Graph Archive: A Community-Driven Effort

In order to evaluate, compare, and tune graph algorithms, experiments on well designed benchmark sets have to be performed. Together with the goal of reproducibility of experimental results, this creates a demand for a public archive to gather and store graph instances. Such an archive would ideally allow annotation of instances or sets of graphs with additional information like graph properties and references to the respective experiments and results. Here we examine the requirements, and introduce a new community project with the aim of producing an easily accessible library of graphs. Through successful community involvement, it is expected that the archive will contain a representative selection of both real-world and generated graph instances, covering significant application areas as well as interesting classes of graphs.Comment: 10 page

Maximizing the Total Resolution of Graphs

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node (angular resolution) or by the angles formed at edge crossings (crossing resolution). In this paper, we evaluate both by introducing the notion of "total resolution", that is, the minimum of the angular and crossing resolution. To the best of our knowledge, this is the first time where the problem of maximizing the total resolution of a drawing is studied. The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings). In addition, we present and experimentally evaluate a force-directed based algorithm that constructs drawings of large total resolution

Subgraph Induced Connectivity Augmentation

Given a planar graph G=(V,E) and a vertex set Wsubseteq V , the subgraph induced planar connectivity augmentation problem asks for a minimum cardinality set F of additional edges with end vertices in W such that G'=(V,Ecup F) is planar and the subgraph of G' induced by W is connected. The problem arises in automatic graph drawing in the context of c -planarity testing of clustered graphs. We describe a linear time algorithm based on SPQR-trees that tests if a subgraph induced planar connectivity augmentation exists and, if so, constructs an minimum cardinality augmenting edge set

A New Approach for Visualizing UML Class Diagrams

UML diagrams have become increasingly important in the engineering and reengineering processes for software systems. Of particular interest are UML class diagrams whose purpose is to display class hierarchies (generalizations), associations, aggregations, and compositions in one picture. The combination of hierarchical and non-hierarchical relations poses a special challenge to a graph layout tool. Existing layout tools treat hierarchical and non-hierarchical relations either alike or as separate tasks in a two-phase process as in, e.g., cite{See97}. We suggest a new approach for visualizing UML class diagrams leading to a balanced mixture of the following aesthetic criteria: Crossing minimization, bend minimization, uniform direction within each class hierarchy, no nesting of one class hierarchy within another, orthogonal layout, merging of multiple inheritance edges, and good edge labelling. We have realized our approach within the graph drawing library GoVisual. Experiments show the superiority to state-of-the-art and industrial standard layouts