On-line Planar Graph Embedding

On-Line Planar Graph Embedding

We present a dynamic data structure for the incremental construction of a planar embedding of a planar graph. The data structure supports the following Ž . operations: i testing if a new edge can be added to the embedding without Ž . introducing crossing; and ii adding vertices and edges. The time complexity of Ž . Ž . each operation is O log n amortized for edge insertion , and the memory spac...

On Embedding an Outer - Planar Graph in aPoint

Given an n-vertex outer-planar graph G and a set P of n points in the plane, we present an O(n log 3 n) time and O(n) space algorithm to compute a straight-line embedding of G in P, improving upon the algorithm in GMPP91, CU96] that requires O(n 2) time. Our algorithm is near-optimal as there is an (n log n) lower bound for the problem BMS95]. We present a simpler O(nd) time and O(n) space algo...

On Embedding an Outer-Planar Graph in a Point Set

On a planar matching in line segments endpoints visibility graph

We show that the segment endpoint visibility graph of any finite set of 2n line segments contains a planar matching that does not use any segment edge, if the line segments in our set are convexly independent.

On Simultaneous Graph Embedding

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another where the mapping is not given. In particular, we show that without mapping, any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar gra...