Embedding a balanced binary tree on a bounded point set

TL;DR

This paper introduces an efficient algorithm for embedding a balanced binary tree onto a set of points within a polygon, ensuring planarity and bounded edge bends, with applications in graph visualization.

Contribution

The paper presents a novel algorithm for embedding balanced binary trees on point sets within polygons, optimizing for planarity and edge bends.

Findings

Algorithm runs in O(m^2 + n(log n)^2 + mn) time.

Embedding maintains planarity with at most O(m) bends per edge.

Applicable to planar graph visualization within polygonal boundaries.

Abstract

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 for embedding an n-vertex balanced binary tree BBT on a set S of n points bounded by a simple m-gon P in O(m^2 + n(log n)^2 + mn) time with at most O(m) bends per edge.