Crossing minimization in perturbed drawings

Radoslav Fulek () and Csaba D. Tóth ()
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Radoslav Fulek: University of Arizona
Csaba D. Tóth: California State University Northridge

Journal of Combinatorial Optimization, No 0, 24 pages

Abstract: Abstract Due to data compression or low resolution, nearby vertices and edges of a graph drawn in the plane may be bundled to a common node or arc. We model such a “compromised” drawing by a piecewise linear map $$\varphi :G\rightarrow {\mathbb {R}}^2$$φ:G→R2. We wish to perturb $$\varphi $$φ by an arbitrarily small $$\varepsilon >0$$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 $$\varepsilon $$ε-perturbation, for every $$\varepsilon >0$$ε>0, is given by a piecewise linear map $$\psi _\varepsilon :G\rightarrow {\mathbb {R}}^2$$ψε:G→R2 with $$\Vert \varphi -\psi _\varepsilon \Vert

Keywords: Map approximation; C-planarity; Crossing number; NP-hardness; 05C10; 05C38; 68R10 (search for similar items in EconPapers)
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DOI: 10.1007/s10878-020-00586-0

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