## On-Line Convex Planarity Testing (1995)

Citations: | 6 - 3 self |

### BibTeX

@MISC{Battista95on-lineconvex,

author = {Giuseppe Di Battista and Roberto Tamassia and Luca Vismara},

title = {On-Line Convex Planarity Testing},

year = {1995}

}

### OpenURL

### Abstract

An important class of planar straight-line drawings of graphs are the convex drawings, in which all faces are drawn as convex polygons. A graph is said to be convex planar if it admits a convex drawing. We consider the problem of testing convex planarity in a semidynamic environment, where a graph is subject to on-line insertions of vertices and edges. We present on-line algorithms for convex planarity testing with the following performance, where t denotes the number of vertices of the graph: convex planarity testing and insertion of vertices take 0(1) worst-case tinhe, insertion of edges takes 0(log n) amortized tinhe, and the space requirement of the data structure is O(n). Furthermore, we give a new combinatorial characterization of convex planar graphs.