Crossing minimization in perturbed drawings

Download (ext.)

Conference Paper | Published | English

Scopus indexed
Author
Fulek, RadoslavISTA ; Tóth, Csaba D.
Department
Series Title
LNCS
Abstract
Due to data compression or low resolution, nearby vertices and edges of a graph drawing may be bundled to a common node or arc. We model such a “compromised” drawing by a piecewise linear map φ:G → ℝ. We wish to perturb φ by an arbitrarily small ε>0 into a proper drawing (in which the vertices are distinct points, any two edges intersect in finitely many points, and no three edges have a common interior point) that minimizes the number of crossings. An ε-perturbation, for every ε>0, is given by a piecewise linear map (Formula Presented), where with ||·|| is the uniform norm (i.e., sup norm). We present a polynomial-time solution for this optimization problem when G is a cycle and the map φ has no spurs (i.e., no two adjacent edges are mapped to overlapping arcs). We also show that the problem becomes NP-complete (i) when G is an arbitrary graph and φ has no spurs, and (ii) when φ may have spurs and G is a cycle or a union of disjoint paths.
Publishing Year
Date Published
2018-12-18
Publisher
Springer
Volume
11282
Page
229-241
Conference
GD: Graph Drawing and Network Visualization
Conference Location
Barcelona, Spain
Conference Date
2018-09-26 – 2018-09-28
IST-REx-ID
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data ISTA Research Explorer

Web of Science

View record in Web of Science®

Sources

arXiv 1808.07608

Search this title in

Google Scholar
ISBN Search