Luca Vismara

Output-Sensitive Reporting of Disjoint Paths

Abstract. A k -path query on a graph consists of computing k vertex-disjoint paths between two given vertices of the graph, whenever they exist. In this paper we study the problem of performing k -path queries, with n

Angles of Planar Triangular Graphs

k leq 3

Turn-Regularity and Optimal Area Drawings of Orthogonal Representations

, in a graph G with n vertices. We denote with n

InteractiveGiotto: An Algorithm for Interactive Orthogonal Graph Drawing

ell

DRAWING DIRECTED ACYCLIC GRAPHS: AN EXPERIMENTAL STUDY

the total length of the reported paths. For n

Angles of planar triangular graphs

k leq 3

Experimental studies on graph drawing algorithms

, we present an optimal data structure for G that uses O(n) space and executes k -path queries in output-sensitive n

A Case Study in Algorithm Engineering for Geometric Computing

O(ell)

Drawing Directed Acyclic Graphs: An Experimental Study

time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st ) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.

GD-Workbench: A System for Prototyping and Testing Graph Drawing Algorithms

We give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating its angles; we also discuss minimality properties of the characterization. The characterization can be used: (1) to decide in linear time whether a given distribution of angles between the edges of a planar triangular graph can result in a planar drawing; (2) to reduce the problem of maximizing the minimum angle in a planar straight-line drawing of a planar triangular graph to a nonlinear optimization problem purely on a space of angles; (3) to give a characterization of the planar drawings of a triconnected graph through a system of equations and inequalities relating its angles; (4) to give a characterization of Delaunay triangulations through a system of equations and inequalities relating its angles; (5) to give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating the lengths of its edges; in turn, this result allows us to give a new characterization of the disc-packing representations of planar triangular graphs.