## Abstract

We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer ≥0, does G have a strict-orthogonal drawing (i.e., an orthogonal drawing without edge bends) with at most k reflex angles per face? For =0, the problem is equivalent to realizing each face as a rectangle. We prove that the strict-orthogonal drawability problem for arbitrary reflex complexity k can be reduced to a graph matching or a network flow problem. Consequently, we obtain an ˜(n^{10/7}k^{1/7})-time algorithm to decide strict-orthogonal drawability, where O˜(r) denotes O(rlog^{c}r), for some constant c. In contrast, if the embedding is not fixed, we prove that it is NP-complete to decide whether a planar graph admits a strict-orthogonal drawing with reflex face complexity 4.

Original language | English (US) |
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Pages (from-to) | 40-52 |

Number of pages | 13 |

Journal | Computational Geometry: Theory and Applications |

Volume | 63 |

DOIs | |

State | Published - Jun 1 2017 |

## Keywords

- Face complexity
- Graph drawing
- Orthogonal drawing

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics