Bend-Minimum Orthogonal Drawings in Quadratic Time
Let G be a planar 3-graph (i.e., a planar graph with vertex degree at most three) with n vertices. We present the first $$O(n^2)$$ -time algorithm that computes a planar orthogonal drawing of G with the minimum number of bends in the variable embedding setting. If either a distinguished edge or a di...
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| Published in | Graph Drawing and Network Visualization Vol. 11282; pp. 481 - 494 |
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| Main Authors | , , |
| Format | Book Chapter |
| Language | English |
| Published |
Switzerland
Springer International Publishing AG
2018
Springer International Publishing |
| Series | Lecture Notes in Computer Science |
| Online Access | Get full text |
| ISBN | 9783030044138 3030044130 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-030-04414-5_34 |
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| Summary: | Let G be a planar 3-graph (i.e., a planar graph with vertex degree at most three) with n vertices. We present the first $$O(n^2)$$ -time algorithm that computes a planar orthogonal drawing of G with the minimum number of bends in the variable embedding setting. If either a distinguished edge or a distinguished vertex of G is constrained to be on the external face, a bend-minimum orthogonal drawing of G that respects this constraint can be computed in O(n) time. Different from previous approaches, our algorithm does not use minimum cost flow models and computes drawings where every edge has at most two bends. |
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| Bibliography: | Original Abstract: Let G be a planar 3-graph (i.e., a planar graph with vertex degree at most three) with n vertices. We present the first \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^2)$$\end{document}-time algorithm that computes a planar orthogonal drawing of G with the minimum number of bends in the variable embedding setting. If either a distinguished edge or a distinguished vertex of G is constrained to be on the external face, a bend-minimum orthogonal drawing of G that respects this constraint can be computed in O(n) time. Different from previous approaches, our algorithm does not use minimum cost flow models and computes drawings where every edge has at most two bends. Research supported in part by the project: “Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni - Ricerca di Base 2018, Dipartimento di Ingegneria dell’Università degli Studi di Perugia” and by MIUR project “MODE – MOrphing graph Drawings Efficiently”, prot. 20157EFM5C_001. |
| ISBN: | 9783030044138 3030044130 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-030-04414-5_34 |