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1 Introduction

This year, the Graph Drawing Contest was divided into two parts: the creative topics and the live challenge.

The creative topics had two graphs: the first one was a graph of inclusion relations between different graph classes, and the second one was a state-transition graph for the game Tic-Tac-Toe. The data sets for the creative topics were published months in advance, and contestants could solve and submit their results before the conference started. The submitted drawings were evaluated according to aesthetic appearance, domain-specific requirements, and how well the data was visually represented.

The live challenge took place during the conference in a format similar to a typical programming contest. Teams were presented with a collection of challenge graphs and had one hour to submit their highest scoring drawings. This year’s topic was to minimize the number of crossings in book layouts with a fixed number of pages.

Overall, we received 25 submissions: 13 submissions for the creative topics and 12 submissions for the live challenge.

2 Creative Topics

The two creative topics for this year were a graph of graph classes, and a tic-tac-toe state graph. The goal was to visualize each graph with complete artistic freedom, and with the aim of communicating the data in the graph as well as possible.

We received 6 submissions for the first topic, and 7 for the second. For each topic, we selected three contenders for the prize, which were printed on large poster boards and presented at the Graph Drawing Symposium. Finally, out of those three, we selected the winning submission. We will now review the top three submissions for each topic (for a complete list of submissions, refer to

2.1 Graph Classes

The Information System on Graph Classes and their Inclusions (ISGCI)Footnote 1 is an initiative to provide a large database of graph classes and their relations, as well as the complexity of several problems that are hard on general graphs. So far, data of 1,511 graph classes and 179,111 inclusions has been collected.

For the first creative topic, participants needed to draw the graph of the graph classes provided by the ISGCI database that are planar. Each node represents a graph class, and each (directed) edge represents an inclusion. For example, the edge from “outerplanar” to “cactus” says that every cactus is outerplanar.

The graph has 65 vertices and 101 edges. The graph is presented in the GraphML File FormatFootnote 2.

The resulting layout of the graph should contain the label of the vertices, provided as the description of the nodes, and should give a good overview on the hierarchy of the graph classes.

Runner-Up: Evmorfia Argyriou, Michael Baur, Anne Eberle, and Martin Siebenhaller (yWorks). The committee liked the use of edge grouping for nodes with many outgoing edges (such as the “planar” node and the use

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of visual bridges to reduce the visual ambiguity at crossings. Also, the drawing makes good use of the available space and uses color as an additional cue to encode distance from the root.

Runner-Up: Megah Fadhillah (University of Sydney). The committee really liked the idea of having a large ”planar” node at the top, which acts as a title for the drawing and immediately explains what is being shown. The drawing uses color to show clusters of nodes and size to encode distance from the root.

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Winner: Tamara Mchedlidze (Karlsruhe Institute of Technology). The committee likes the visual appeal of the drawing. The use of circular arcs for edges makes it easy to follow each individual edge, even when they pass behind

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vertices (something which is traditionally considered bad practice in graph drawing). The drawing uses color to single out three meaningful groups of nodes: tree classes, bounded degree classes, and grid-like classes. The author also put a lot of thought into abbreviating node labels to increase the readability of the final drawing.

2.2 Tic-Tac-Toe

Tic-Tac-ToeFootnote 3 is a tactical two-player game in which two players take turns entering symbols (X or O) into cells of a three-by-three grid, with the objective of creating a row, column, or diagonal of equal symbols. The game is famous for its relative simplicity.

For the second creative topic, participants were asked to draw the graph of all possible Tic-Tac-Toe game states, in a way that shows as much of the structure and hidden information in the graph as possible. Each node represents a class of symmetric board positions, and there is an edge between two nodes u and v if a board position from v can be reached from a board position from u.

Runner-Up: Remus Zelina, Sebastian Bota, Siebren Houtman, and Radu Balaban (Meurs). The committee really liked visual appeal of the full drawing, which clusters the individual node into groups based on the ply (number of moves played) and the current winner after optimal play. This way, the drawing clearly shows a much smaller meta-graph (25 nodes and 39 edges) with

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colors encoding the game state and “size” of clusters encoding the number of actual board positions that belong to that state. This drawing nicely communicates the global structure of the game.

Runner-Up: Evmorfia Argyriou, Michael Baur, Anne Eberle, and Martin Siebenhaller (yWorks). The second runner-up submitted an interactive visualization of the graphFootnote 4. The committee liked the idea of using an interactive tool to explore the state graph. Using the tool, you can really see the impact of each move, making it very useful for understanding the game. The tool will dynamically show the local neighborhood (all possible paths to get to the situation, and all possible continuations) for any board position. Using small colored disks, the winner after optimal play is visualized for individual nodes.

Winner: Jennifer Hood and Pat Morin (Carleton University). The committee was impressed by the way this drawing manages to illustrate the global structure of the graph while still making it possible to follow individual paths and board positions. The global structure is nicely visualized by presenting the nodes in three columns, indicating which player will win upon optimal play, and nine rows, indicating the ply of the positions. Edge colors distinguish between move types (optimal or non-optimal, which player made the move, and which player wins). The committee especially liked the use of variable node sizes, making them small where necessary without affecting other parts of the

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drawing. Similarly, the committee liked the use of solid edges for the (relatively) small set of optimal-play edges and more faded colors for the non-optimal-play edges. Presenting the optimal-play edges (straight) in a different style than the non-optimal-play edges (orthogonal) further enhances their visual distinction.

3 Live Challenge

The live challenge took place during the conference and lasted exactly one hour. During this hour, local participants of the conference could take part in the manual category (in which they could attempt to solve the graphs using a supplied tool), or in the automatic category (in which they could use their own software to solve the graphs). At the same time, remote participants could also take part in the automatic category.

The challenge focused on minimizing the number of crossings in a book embedding with k pages. The input graphs are arbitrary undirected graphs and a maximum number of pages that may be used.

A book with k pages consists of k half-spaces, the pages, that share a single line, the spine of the book. A k-page book embedding of a graph is an embedding of a graph into a book with k pages such that all the vertices lie at distinct positions of the spine and every edge is drawn in one of the pages such that only its endpoints touch the spine.

Note that edges may only cross if they are assigned to the same page. We are looking for drawings that minimize the number of crossings. The results are judged solely with respect to the number of crossings; other aesthetic criteria are not taken into account. This allows an objective way to qualitatively evaluate a given drawing.

3.1 Manual Category

In the manual category, participants were presented with five graphs. These were arranged from small to large and chosen to highlight different types of graphs and graph structures. For illustration, we include the first graph in its initial state and the best manual solution we received (by team snowman). For the complete set of graphs and submissions, refer to the contest website.

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We are happy to present the full list of scores for all teams. The numbers listed are the number of crossings in each graph; the horizontal bars visualize the corresponding scores.

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The winning team is team snowman, consisting of Boris Klemz, Ulf Rüegg, and Fabian Lipp!

3.2 Automatic Category

In the automatic category, participants had to solve the same five graphs as in the manual category, and in addition another five—much larger—graphs. Again, the graphs were constructed to have different structure.

Once more, for illustration, we include the first large graph as it looks in the tool. The graphs themselves can be found on the contest website.

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The winning team is team Pepa, consisting of Josef Cibulka!