Resistance distance in straight linear 2-trees

A Linear Tree Edit Distance Algorithm for Similar Ordered Trees

We describe a linear algorithm for comparing two similar ordered rooted trees with node labels. The method for comparing trees is the usual tree edit distance. We show that an optimal mapping which uses at most k insertions or deletions can then be constructed in O(nk) where n is the size of the trees. The approach is inspired by the ZhangShasha algorithm for tree edit distance in combination w...

Linear and cyclic distance-three labellings of trees

Given a finite or infinite graph G and positive integers `, h1, h2, h3, an L(h1, h2, h3)labelling of G with span ` is a mapping f : V (G) → {0, 1, 2, . . . , `} such that, for i = 1, 2, 3 and any u, v ∈ V (G) at distance i in G, |f(u)−f(v)| ≥ hi. A C(h1, h2, h3)-labelling of G with span ` is defined similarly by requiring |f(u)− f(v)|` ≥ hi instead, where |x|` = min{|x|, `− |x|}. The minimum sp...

Representing Directed Trees as Straight Skeletons

The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be...

3D Straight-line Drawings of k-trees

This paper studies the problem of computing 3D crossing-free straight-line grid drawings of graphs such that the overall volume is small. We show that every 2-tree (and therefore every series-parallel graph) can be drawn on an integer 3D grid consisting of 15 parallel lines and having linear volume. We extend the study to the problem of drawing general k-trees on a set of parallel grid lines. L...

Orthogonal Straight Line Drawing of Trees