Bundled Crossings Revisited

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

doi:10.1007/978-3-030-35802-0_5

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: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › 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) when we require a simple circular layout. These results make use of the connection between bundled crossings and graph genus.

Original language	English
Title of host publication	Graph Drawing and Network Visualization. GD 2019
Editors	D. Archambault, C. Tóth
Pages	63-77
Number of pages	15
ISBN (Electronic)	978-3-030-35802-0
DOIs	https://doi.org/10.1007/978-3-030-35802-0_5
Publication status	Published - 2019
Externally published	Yes

Publication series

Series	Lecture Notes in Computer Science
Volume	11904
ISSN	0302-9743

Keywords

EMBEDDING GRAPHS
GENUS
LINEAR-TIME ALGORITHM
VISUALIZATION

Access to Document

10.1007/978-3-030-35802-0_5

1 Article

Bundled Crossings Revisited
Chaplick, S., Dijk, T. C. V., Kryven, M., Park, J., Ravsky, A. & Wolff, A., 2020, In: Journal of Graph Algorithms and Applications. 24, 4, p. 621-655 35 p.
Research output: Contribution to journal › Article › Academic › peer-review

Open Access

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) when we require a simple circular layout. These results make use of the connection between bundled crossings and graph genus.",

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