Bundled Crossings Revisited

Steven Chaplick; Thomas C. van Dijk; Myroslav Kryven; Ji-won Park; Alexander Ravsky; Alexander Wolff

doi:10.7155/jgaa.00535

Bundled Crossings Revisited

Steven Chaplick^*, Thomas C. van Dijk, Myroslav Kryven, Ji-won Park, Alexander Ravsky, Alexander Wolff

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into bundles. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between two bundles, i.e., as a bundled crossing. We consider the problem of bundled crossing minimization: A graph is given and the goal is to find a bundled drawing with at most k bundled crossings. We show that the problem is NP-hard when we require a simple drawing. Our main result is an FPT algorithm (in k) for simple circular layouts where vertices must be placed on a circle and edges must be drawn inside the circle. These results make use of the connection between bundled crossings and graph genus. We also consider bundling crossings in a given drawing, in particular for storyline visualizations.

Original language	English
Pages (from-to)	621-655
Number of pages	35
Journal	Journal of Graph Algorithms and Applications
Volume	24
Issue number	4
DOIs	https://doi.org/10.7155/jgaa.00535
Publication status	Published - 2020

Keywords

LINEAR-TIME ALGORITHM
EMBEDDING GRAPHS
VISUALIZATION
GENUS

Access to Document

10.7155/jgaa.00535Licence: CC BY

1 Conference article in proceeding
1 Preprint

Bundled Crossings Revisited
Chaplick, S., Dijk, T. C. V., Kryven, M., Park, J., Ravsky, A. & Wolff, A., 2019, Graph Drawing and Network Visualization. GD 2019. Archambault, D. & Tóth, C. (eds.). p. 63-77 15 p. (Lecture Notes in Computer Science, Vol. 11904).
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review
Bundled Crossings Revisited
Chaplick, S., Dijk, T. C. V., Kryven, M., Park, J., Ravsky, A. & Wolff, A., 2018, 20 p.
Research output: Working paper / Preprint › Preprint

Cite this

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title = "Bundled Crossings Revisited",

abstract = "An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into bundles. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between two bundles, i.e., as a bundled crossing. We consider the problem of bundled crossing minimization: A graph is given and the goal is to find a bundled drawing with at most k bundled crossings. We show that the problem is NP-hard when we require a simple drawing. Our main result is an FPT algorithm (in k) for simple circular layouts where vertices must be placed on a circle and edges must be drawn inside the circle. These results make use of the connection between bundled crossings and graph genus. We also consider bundling crossings in a given drawing, in particular for storyline visualizations.",

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