Splitting Vertices in 2-Layer Graph Drawings
Ahmed, Reyan Angelini, Patrizio
Bekos, Michael A. Di Battista, Giuseppe Kaufmann, Michael Kindermann, Philipp Kobourov, Stephen G. Nöllenburg, Martin Symvonis, Antonios Villedieu, Anaïs
Ahmed, Reyan
Bekos, Michael A.
Di Battista, Giuseppe
Kaufmann, Michael
Kindermann, Philipp
Kobourov, Stephen G.
Nöllenburg, Martin
Symvonis, Antonios
Villedieu, Anaïs
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Abstract
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines (layers), and their relationships (edges) are represented by segments connecting vertices. Methods for constructing 2-layer drawings often try to minimize the number of edge crossings. We use vertex splitting to reduce the number of crossings, by replacing selected vertices on one layer by two (or more) copies and suitably distributing their incident edges among these copies. We study several optimization problems related to vertex splitting, either minimizing the number of crossings or removing all crossings with fewest splits. While we prove that some variants are NPNP-complete, we obtain polynomial-time algorithms for others. We run our algorithms on a benchmark set of bipartite graphs representing the relationships between human anatomical structures and cell types.
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Date
2023
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Publisher
IEEE
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Keywords
Bipartite graph, Graph drawing, Optimization, Visualization, Layout, Approximation algorithms, Minimization
Citation
Ahmed, Reyan, Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Michael Kaufmann, Philipp Kindermann, Stephen Kobourov, et al. “Splitting Vertices in 2-Layer Graph Drawings.” IEEE Computer Graphics and Applications 43 (3): 24-35. 2023.