Straight-line programs offer powerful text compression by representing a text T [1, u] in terms of a context-free grammar of n rules, so that T can be recovered in O(u) time. However, the problem of operating the grammar in compressed form has not been studied much. We present the first grammar representation able of extracting text substrings, and of searching the text for patterns, in time o(...

A straight line triangle representation (SLTR) of a planar graph is a straight line drawing such that all the faces including the outer face have triangular shape. Such a drawing can be viewed as a tiling of a triangle using triangles with the input graph as skeletal structure. In this paper we present a characterization of graphs that have an SLTR. The charcterization is based on flat angle as...

We introduce the concept of a constrained pointed pseudo-triangulation TG of a point set S with respect to a pointed planar straight line graph G = (S,E). For the case that G forms a simple polygon P with vertex set S we give tight bounds on the vertex degree of TG.

It is shown that if a planar straight line graph (PSLG) with n vertices in general position in the plane can be augmented to a 3-edge-connected PSLG, then 2n−2 new edges are enough for the augmentation. This bound is tight: there are PSLGs with n ≥ 4 vertices such that any augmentation to a 3-edge-connected PSLG requires 2n− 2 new edges.

It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph by adding at most bn/2c edge...

Let G be a cycle-free connected straight-line graph with predefined edge lengths and fixed order of incident edges around each vertex. We address the problem of deciding whether there exists a simple polygon P such that G is the straight skeleton of P . We show that for given G such a polygon P might not exist, and if it exists it might not be unique. For the later case we give an example with ...

Luca Vismara — 10.

This article introduces a straight-line drawing algorithm for quadrangulations, in the family of the face-counting algorithms. It outputs in linear time a drawing on a regular W×H grid such that W+H = n − 1 −∆, where n is the number of vertices and ∆ is an explicit combinatorial parameter of the quadrangulation.