On embedding an outer-planar graph in a point set

On Embedding an Outer-Planar Graph in a Point Set

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-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...

Embedding a balanced binary tree on a bounded point set

Given an undirected planar graph G with n vertices and a set S of n points inside a simple polygon P , a point-set embedding of G on S is a planar drawing of G such that each vertex is mapped to a distinct point of S and the edges are polygonal chains surrounded by P . A special case of the embedding problem is that in which G is a balanced binary tree. In this paper, we present a new algorithm...

On the maximum area pentagon in a planar point set

A finite set of points in the plane is described as in convex position if it forms the set of vertices of a convex polygon. This work studies the ratio between the maximum area of convex heptagons with vertices in P and the area of the convex hull of P, where the planar point set P is in convex position.