On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Planar L-Drawings of Directed Graphs

We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upward-planar L-drawings. We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering. We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

An energy-based model to optimize cluster visualization

National audienceGraphs are mathematical structures that provide natural means for complex-data representation. Graphs capture the structure and thus help modeling a wide range of complex real-life data in various domains. Moreover graphs are especially suitable for information visualization. Indeed the intuitive visualabstraction (dots and lines) they provide is intimately associated with graphs. Visualization paves the way to interactive exploratory data-analysis and to important goals such as identifying groups and subgroups among data and helping to understand how these groups interact with each other. In this paper, we present a graph drawing approach that helps to better appreciate the cluster structure in data and the interactions that may exist between clusters. In this work, we assume that the clusters are already extracted and focus rather on the visualization aspects. We propose an energy-based model for graph drawing that produces an esthetic drawing that ensures each cluster will occupy a separate zone within thevisualization layout. This method emphasizes the inter-groups interactions and still shows the inter-nodes interactions. The drawing areas assigned to the clusters can be user-specified (prefixed areas) or automatically crafted (free areas). The approach we suggest also enables handling geographically-based clustering. In the case of free areas, we illustrate the use of our drawing method through an example. In the case of prefixed areas, we firstuse an example from citation networks and then use another exampleto compare the results of our method to those of the divide and conquer approach. In the latter case, we show that while the two methods successfully point out the cluster structure our method better visualize the global structure

The DFS-heuristic for orthogonal graph drawing☆☆Some of these result were published in the author's PhD thesis at Rutgers University; the author would like to thank her advisor, Prof. Endre Boros, for much helpful input. The results in Section 5 have been presented at the 8th Canadian Conference on Computational Geometry, Ottawa, 1996, see [1].

AbstractIn this paper, we present a new heuristic for orthogonal graph drawings, which creates drawings by performing a depth-first search and placing the nodes in the order they are encountered. This DFS-heuristic works for graphs with arbitrarily high degrees, and particularly well for graphs with maximum degree 3. It yields drawings with at most one bend per edge, and a total number of m−n+1 bends for a graph with n nodes and m edges; this improves significantly on the best previous bound of m−2 bends

Graph layout for applications in compiler construction

We address graph visualization from the viewpoint of compiler construction. Most data structures in compilers are large, dense graphs such as annotated control flow graph, syntax trees, dependency graphs. Our main focus is the animation and interactive exploration of these graphs. Fast layout heuristics and powerful browsing methods are needed. We give a survey of layout heuristics for general directed and undirected graphs and present the browsing facilities that help to manage large structured graph

Planar L-Drawings of Bimodal Graphs

In a planar L-drawing of a directed graph (digraph) each edge e is represented as a polyline composed of a vertical segment starting at the tail of e and a horizontal segment ending at the head of e. Distinct edges may overlap, but not cross. Our main focus is on bimodal graphs, i.e., digraphs admitting a planar embedding in which the incoming and outgoing edges around each vertex are contiguous. We show that every plane bimodal graph without 2-cycles admits a planar L-drawing. This includes the class of upward-plane graphs. Finally, outerplanar digraphs admit a planar L-drawing - although they do not always have a bimodal embedding - but not necessarily with an outerplanar embedding.Comment: Appears in the Proceedings of the 28th International Symposium on Graph Drawing and Network Visualization (GD 2020

Graph layout for applications in compiler construction

We address graph visualization from the viewpoint of compiler construction. Most data structures in compilers are large, dense graphs such as annotated control flow graph, syntax trees, dependency graphs. Our main focus is the animation and interactive exploration of these graphs. Fast layout heuristics and powerful browsing methods are needed. We give a survey of layout heuristics for general directed and undirected graphs and present the browsing facilities that help to manage large structured graph

More compact orthogonal drawings by allowing additional bends

Compacting orthogonal drawings is a challenging task. Usually, algorithms try to compute drawings with small area or total edge length while preserving the underlying orthogonal shape. We suggest a moderate relaxation of the orthogonal compaction problem, namely the one-dimensional monotone flexible edge compaction problem with fixed vertex star geometry. We further show that this problem can be solved in polynomial time using a network flow model. An experimental evaluation shows that by allowing additional bends could reduce the total edge length and the drawing area