## ON-LINE PLANARITY TESTING (1996)

Citations: | 25 - 2 self |

### BibTeX

@MISC{Battista96on-lineplanarity,

author = {Giuseppe Di Battista and Roberto Tamassia},

title = {ON-LINE PLANARITY TESTING},

year = {1996}

}

### OpenURL

### Abstract

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 online 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.