# A dynamic data structure for planar graph embedding

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## Abstract

We present a dynamic data structure that allows for incrementally constructing a planar embedding of a planar graph with *n* vertices and *m* edges. The data structure supports the following operations: (1) testing if a new edge can be added to the embedding without introducing crossings; (2) adding and removing vertices and edges. In each case the time complexity is *O* (log *m*). The space used and the preprocessing time are *O*(*m*). If the graph is simple (i.e. it has no self-loops and no parallel edges), the above bounds become *O*(log *n*) and *O*(*n*), respectively. This work finds applications in circuit layout, graphics, motion planning, and computer-aided design.

## Keywords

Plane Graph Outgoing Edge Parallel Edge Embedding Problem Planar Embedding
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1988