Level-Planar Drawings with Few Slopes

We introduce and study level-planar straight-line drawings with a fixed number of slopes. For proper level graphs (all edges connect vertices of adjacent levels), we give an ( log$^{2}$ / log log )-time algorithm that either finds such a drawing or determines that no such drawing exists. Moreover, we consider the partial drawing extension problem, where we seek to extend an immutable drawing of a subgraph to a drawing of the whole graph, and the simultaneous drawing problem, which asks about the existence of drawings of two graphs whose restrictions to their shared subgraph coincide. We present ($^{4/3}$ log )-time and ($^{10/3}$ log )-time algorithms for these respective problems on proper level-planar graphs. We complement these positive results by showing that testing whether non-proper level graphs admit level-planar drawings with slopes is NP-hard even in restricted cases

Cubic Planar Graphs That Cannot Be Drawn On Few Lines

For every integer l, we construct a cubic 3-vertex-connected planar bipartite graph G with O(l^3) vertices such that there is no planar straight-line drawing of G whose vertices all lie on l lines. This strengthens previous results on graphs that cannot be drawn on few lines, which constructed significantly larger maximal planar graphs. We also find apex-trees and cubic bipartite series-parallel graphs that cannot be drawn on a bounded number of lines

Flud: a hybrid crowd-algorithm approach for visualizing biological networks

Modern experiments in many disciplines generate large quantities of network (graph) data. Researchers require aesthetic layouts of these networks that clearly convey the domain knowledge and meaning. However, the problem remains challenging due to multiple conflicting aesthetic criteria and complex domain-specific constraints. In this paper, we present a strategy for generating visualizations that can help network biologists understand the protein interactions that underlie processes that take place in the cell. Specifically, we have developed Flud, an online game with a purpose (GWAP) that allows humans with no expertise to design biologically meaningful graph layouts with the help of algorithmically generated suggestions. Further, we propose a novel hybrid approach for graph layout wherein crowdworkers and a simulated annealing algorithm build on each other's progress. To showcase the effectiveness of Flud, we recruited crowd workers on Amazon Mechanical Turk to lay out complex networks that represent signaling pathways. Our results show that the proposed hybrid approach outperforms state-of-the-art techniques for graphs with a large number of feedback loops. We also found that the algorithmically generated suggestions guided the players when they are stuck and helped them improve their score. Finally, we discuss broader implications for mixed-initiative interactions in human computation games.Comment: This manuscript is currently under revie

On L-shaped point set embeddings of trees : first non-embeddable examples

An L-shaped embedding of a tree in a point set is a planar drawing of the tree where the vertices are mapped to distinct points and every edge is drawn as a sequence of two axis-aligned line segments. There has been considerable work on establishing upper bounds on the minimum cardinality of a point set to guarantee that any tree of the same size with maximum degree 4 admits an L-shaped embedding on the point set. However, no non-trivial lower bound is known to this date, i.e., no known n-vertex tree requires more than n points to be embedded. In this paper, we present the first examples of n-vertex trees for n∈{13,14,16,17,18,19,20} that require strictly more points than vertices to admit an L-shaped embedding. Moreover, using computer help, we show that every tree on n≤12 vertices admits an L-shaped embedding in every set of n points. We also consider embedding ordered trees, where the cyclic order of the neighbors of each vertex in the embedding is prescribed. For this setting, we determine the smallest non-embeddable ordered tree on n=10 vertices, and we show that every ordered tree on n≤9 or n=11 vertices admits an L-shaped embedding in every set of n points. We also construct an infinite family of ordered trees which do not always admit an L-shaped embedding, answering a question raised by Biedl, Chan, Derka, Jain, and Lubiw

Graph Algorithms and Applications

The mixture of data in real-life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. This book contains some papers reporting recent achievements regarding graph models, algorithms, and applications to problems in the real world, with some focus on optimization and computational complexity

Languages of games and play: A systematic mapping study

Digital games are a powerful means for creating enticing, beautiful, educational, and often highly addictive interactive experiences that impact the lives of billions of players worldwide. We explore what informs the design and construction of good games to learn how to speed-up game development. In particular, we study to what extent languages, notations, patterns, and tools, can offer experts theoretical foundations, systematic techniques, and practical solutions they need to raise their productivity and improve the quality of games and play. Despite the growing number of publications on this topic there is currently no overview describing the state-of-the-art that relates research areas, goals, and applications. As a result, efforts and successes are often one-off, lessons learned go overlooked, language reuse remains minimal, and opportunities for collaboration and synergy are lost. We present a systematic map that identifies relevant publications and gives an overview of research areas and publication venues. In addition, we categorize research perspectives along common objectives, techniques, and approaches, illustrated by summaries of selected languages. Finally, we distill challenges and opportunities for future research and development