On-line Planar Graph Embedding

Abstract

We present a dynamic data structure for the incremental construction of a planar embedding of a planar graph. The data structure supports the following operations: (i) testing if a new edge can be added to the embedding without introducing crossing; and (ii) adding vertices and edges. The time complexity of each operation isO(log n) (amortized for edge insertion), and the memory space and preprocessing time areO(n), wherenis the current number of vertices of the graph.