Planar Drawings and Angular Resolution: Algorithms and Bounds (Extended Abstract) (1994)
| Venue: | IN PROC. 2ND ANNU. EUROPEAN SYMPOS. ALGORITHMS |
| Citations: | 22 - 5 self |
BibTeX
@INPROCEEDINGS{Garg94planardrawings,
author = {Ashim Garg and Roberto Tamassia},
title = {Planar Drawings and Angular Resolution: Algorithms and Bounds (Extended Abstract)},
booktitle = {IN PROC. 2ND ANNU. EUROPEAN SYMPOS. ALGORITHMS},
year = {1994},
pages = {12--23},
publisher = {Springer-Verlag}
}
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Abstract
We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straight-line drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on the angular resolution of planar straight-line drawings, and show a continuous trade-off between the area and the angular resolution. We also give linear-time algorithms for constructing planar straight-line drawings with high angular resolution for various classes of graphs, such as series-parallel graphs, outerplanar graphs, and triangulations generated by nested triangles. Our results are obtained by new techniques that make extensive use of geometric constructions.
