TY - JOUR

T1 - Splitting Vertices in 2-Layer Graph Drawings

AU - Ahmed, Reyan

AU - Angelini, Patrizio

AU - Bekos, Michael A.

AU - Battista, Giuseppe Di

AU - Kaufmann, Michael

AU - Kindermann, Philipp

AU - Kobourov, Stephen

AU - Nollenburg, Martin

AU - Symvonis, Antonios

AU - Villedieu, Anais

AU - Wallinger, Markus

N1 - Publisher Copyright:
© 1981-2012 IEEE.

PY - 2023/5/1

Y1 - 2023/5/1

N2 - 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 NP-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.

AB - 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 NP-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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U2 - 10.1109/MCG.2023.3264244

DO - 10.1109/MCG.2023.3264244

M3 - Article

C2 - 37023163

AN - SCOPUS:85153368673

SN - 0272-1716

VL - 43

SP - 24

EP - 35

JO - IEEE Computer Graphics and Applications

JF - IEEE Computer Graphics and Applications

IS - 3

ER -