Fulek, RadoslavIST Austria ; Tóth, Csaba D.
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.
Graph Drawing and Network Visualization
2018-09-26 – 2018-09-28
Fulek R, Tóth CD. Crossing minimization in perturbed drawings. In: Vol 11282. Springer; 2018:229-241. doi:10.1007/978-3-030-04414-5_16
Fulek, R., & Tóth, C. D. (2018). Crossing minimization in perturbed drawings (Vol. 11282, pp. 229–241). Presented at the Graph Drawing and Network Visualization, Barcelona, Spain: Springer. https://doi.org/10.1007/978-3-030-04414-5_16
Fulek, Radoslav, and Csaba D. Tóth. “Crossing Minimization in Perturbed Drawings,” 11282:229–41. Springer, 2018. https://doi.org/10.1007/978-3-030-04414-5_16.
R. Fulek and C. D. Tóth, “Crossing minimization in perturbed drawings,” presented at the Graph Drawing and Network Visualization, Barcelona, Spain, 2018, vol. 11282, pp. 229–241.
Fulek R, Tóth CD. 2018. Crossing minimization in perturbed drawings. Graph Drawing and Network Visualization, LNCS, vol. 11282, 229–241.
Fulek, Radoslav, and Csaba D. Tóth. Crossing Minimization in Perturbed Drawings. Vol. 11282, Springer, 2018, pp. 229–41, doi:10.1007/978-3-030-04414-5_16.