Name
Abstract | ||
|---|---|---|
Given an n-vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous transformation) between the two drawings that preserves straight-line planarity and consists of O(n) steps, which we prove is optimal in the worst case. Each step is a unidirectional linear morph, which means that every vertex moves at constant speed along a straight line, and the lines are parallel although the vertex speeds may differ. Thus we provide an efficient version of Cairns' 1944 proof of the existence of straight-line planarity-preserving morphs for triangulated graphs, which required an exponential number of steps. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1069171 | SIAM JOURNAL ON COMPUTING |
Keywords | DocType | Volume |
planar graphs,transformation,morph | Journal | 46 |
Issue | ISSN | Citations |
2 | 0097-5397 | 5 |
PageRank | References | Authors |
0.59 | 22 | 13 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Soroush Alamdari | 1 | 56 | 5.93 |
| Patrizio Angelini | 2 | 158 | 25.43 |
| Fidel Barrera-Cruz | 3 | 13 | 3.68 |
| Timothy M. Chan | 4 | 2033 | 150.55 |
| Giordano Da Lozzo | 5 | 87 | 23.65 |
| Giuseppe Di Battista | 6 | 2298 | 361.48 |
| Fabrizio Frati | 7 | 462 | 48.60 |
| Penny Haxell | 8 | 7 | 1.34 |
| Anna Lubiw | 9 | 753 | 95.36 |
| Maurizio Patrignani | 10 | 675 | 61.47 |
| Vincenzo Roselli | 11 | 69 | 11.57 |
| Sahil Singla | 12 | 83 | 16.29 |
| Bryan T. Wilkinson | 13 | 43 | 4.18 |