On-Line Planarity Testing

The on-line planarity-testing problem consists of performing the following operations on a planar graph $G$: (i) testing if a new edge can be added to $G$ so that the resulting graph is itself planar; (ii) adding vertices and edges such that planarity is preserved. An efficient technique for on-line planarity testing of a graph is presented that uses $O(n)$ space and supports tests and insertions of vertices and edges in $O(\log n)$ time, where $n$ is the current number of vertices of $G$. The bounds for tests and vertex insertions are worst-case and the bound for edge insertions is amortized. We also present other applications of this technique to dynamic algorithms for planar graphs.

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