Equivalence of Turn-Regularity and Complete Extensions

Alexander M. Esser

2019

Abstract

The aim of the two-dimensional compaction problem is to minimize the total edge length or the area of an orthogonal grid drawing. The coordinates of the vertices and the length of the edges can be altered while all angles and the shape of the drawing have to be preserved. The problem has been shown to be NP-hard. Two commonly used compaction methods are the turn-regularity approach by (Bridgeman et al., 2000) and the approach by (Klau and Mutzel, 1999) considering complete extensions. We formally prove that these approaches are equivalent, i. e. a face of an orthogonal representation is turn-regular if and only if there exists a unique complete extension for the segments bounding this face.

Paper Citation

in Harvard Style

Esser A. (2019). Equivalence of Turn-Regularity and Complete Extensions. In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019) - Volume 3: IVAPP; ISBN 978-989-758-354-4, SciTePress, pages 39-47. DOI: 10.5220/0007353500390047

in Bibtex Style

@conference{ivapp19,
author={Alexander M. Esser},
title={Equivalence of Turn-Regularity and Complete Extensions},
booktitle={Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019) - Volume 3: IVAPP},
year={2019},
pages={39-47},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007353500390047},
isbn={978-989-758-354-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019) - Volume 3: IVAPP
TI - Equivalence of Turn-Regularity and Complete Extensions
SN - 978-989-758-354-4
AU - Esser A.
PY - 2019
SP - 39
EP - 47
DO - 10.5220/0007353500390047
PB - SciTePress