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CrossingMinimization.pdf
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Final Accepted Manuscript
Affiliation
Univ ArizonaIssue Date
2020-06-12Keywords
Computational Theory and MathematicsControl and Optimization
Applied Mathematics
Discrete Mathematics and Combinatorics
Computer Science Applications
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SPRINGERCitation
Fulek, R., Tóth, C.D. Crossing minimization in perturbed drawings. J Comb Optim 40, 279–302 (2020). https://doi.org/10.1007/s10878-020-00586-0Rights
Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2020.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.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 phi:G -> R-2. We wish to perturb phi by an arbitrarily small epsilon>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 epsilon-perturbation, for every epsilon>0, is given by a piecewise linear map psi epsilon:G -> R-2 with ||phi-psi epsilon||<epsilon is the uniform norm (i.e.,supnorm). We present a polynomial-time solution for this optimization problem whenGis a cycle and the map phi has nospurs(i.e., no two adjacent edges are mapped to overlapping arcs). We also show that the problem becomes NP-complete (i) whenGis an arbitrary graph and phi has no spurs, and (ii) when phi may have spurs andGis a cycle or a union of disjoint paths.Note
12 month embargo; published online: 12 June 2020ISSN
1382-6905Version
Final accepted manuscriptae974a485f413a2113503eed53cd6c53
10.1007/s10878-020-00586-0