Confluent Hasse diagrams

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Abstract

We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with \(O(n^2)\) features, in an \(O(n) \times O(n)\) grid in \(O(n^2)\) time. For the digraphs representing series-parallel partial orders we show how to construct a drawing with \(O(n)\) features in an \(O(n) \times O(n)\) grid in \(O(n)\) time from a series-parallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use.

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Hierarchical edge bundles: visualization of adjacency relations in hierarchical data.

Danny Holten (2015)

A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations.