Drawing planar graphs using the canonical ordering
research_article
en
https://scigraph.springernature.com/explorer/license/
http://link.springer.com/10.1007/BF02086606
We introduce a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear-time-and-space algorithms can be designed for many graph-drawing problems. Our main results are as follows:Every triconnected planar graphG admits a planar convex grid drawing with straight lines on a (2n−4)×(n−2) grid, wheren is the number of vertices.Every triconnected planar graph with maximum degree 4 admits a planar orthogonal grid drawing on ann×n grid with at most [3n/2]+4 bends, and ifn>6, then every edge has at most two bends.Every planar graph with maximum degree 3 admits a planar orthogonal grid drawing with at most [n/2]+1 bends on an [n/2]×[n/2] grid.Every triconnected planar graphG admits a planar polyline grid drawing on a (2n−6)×(3n−9) grid with minimum angle larger than 2/d radians and at most 5n−15 bends, withd the maximum degree. Every triconnected planar graphG admits a planar convex grid drawing with straight lines on a (2n−4)×(n−2) grid, wheren is the number of vertices. Every triconnected planar graph with maximum degree 4 admits a planar orthogonal grid drawing on ann×n grid with at most [3n/2]+4 bends, and ifn>6, then every edge has at most two bends. Every planar graph with maximum degree 3 admits a planar orthogonal grid drawing with at most [n/2]+1 bends on an [n/2]×[n/2] grid. Every triconnected planar graphG admits a planar polyline grid drawing on a (2n−6)×(3n−9) grid with minimum angle larger than 2/d radians and at most 5n−15 bends, withd the maximum degree. These results give in some cases considerable improvements over previous results, and give new bounds in other cases. Several other results, e.g., concerning visibility representations, are included.
4-32
1996-07-01
true
2019-04-11T11:56
articles
1996-07
Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands
Utrecht University
Springer Nature - SN SciGraph project
G.
Kant
10.1007/bf02086606
doi
Computation Theory and Mathematics
1
dimensions_id
pub.1024228802
16
Algorithmica
0178-4617
1432-0541
Information and Computing Sciences
736dc031e71a8a2d543144df1e046b14b0b28c422ab2028d266cd16efc2ef6df
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