G. Di Battista

Automatic graph drawing and readability of diagrams

The state of the art in automatic graph drawing is reviewed, with special attention to the readability of information system diagrams. Existing results in the literature are compared, and a comprehensive algorithmic approach to the problem is proposed. The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures. Several applications of GIOTTO, a graphic tool that embodies the aforementioned facility, are shown. >

Computing the types of the relationships between autonomous systems

The problem of computing the types of the relationships between Internet autonomous systems is investigated. We refer to the model introduced in (ref.1), (ref.2) that bases the discovery of such relationships on the analysis of the AS paths extracted from the BGP routing tables. We characterize the time complexity of the above problem, showing both NP-completeness results and efficient algorithms for solving specific cases. Motivated by the hardness of the general problem, we propose heuristics based on a novel paradigm and show their effectiveness against publicly available data sets. The experiments put in evidence that our heuristics performs significantly better than state of the art heuristics.

Incremental planarity testing

The incremental planarity testing problem consists of performing the following operations on a planar graph G with n vertices: (1) testing whether a new edge can be added to G so that the resulting graph is itself planar; (2) adding vertices and edges such that planarity is preserved. An efficient technique for incremental planarity testing that uses O(n) space and supports tests and insertion of vertices and edges in O(log n) time is presented. The bounds for queries and vertex insertions are worst case, and the bound for edge insertions is amortized.<<ETX>>

Upward drawings of triconnected digraphs

A polynomial-time algorithm for testing if a triconnected directed graph has an upward drkwing is presented. An upward drkwing is a planar drkwing such that all the edges flow in a common direction (e.g., from bottom to top). The problem arises in the fields of automatic graph drkwing and ordered sets, and has been open for several years. The proposed algorithm is based on a new combinatorial characterization that maps the problem into a max-flow problem on a sparse network; the time complexity isO(n+r2), wheren is the number of vertices andr is the number of sources and sinks of the directed graph. If the directed graph has an upward drkwing, the algorithm allows us to construct one easily.

A note on optimal area algorithms for upward drawings of binary trees

The goal of this paper is to investigate the area requirements for upward grid drawings of binary trees. First, we show that there is a family of binary trees with n vertices that require ω(n log n) area; this bound is tight to within a constant factor, i.e. any binary tree with n vertices can be drawn in O(n log n) area. Then we present an algorithm for constructing an upward drawing of a complete binary tree with n vertices in O(n) area, and, finally, we extend this result to the drawings of Fibonacci trees.

Structuring primitives for a dictionary of entity relationship data schemas

The data dictionary contains the description of all types of data produced, managed, exchanged, and maintained in an organization. Data descriptions (very often hundreds of schemas) should be organized in such a way to allow all the users of the information system to understand the meaning of data and their relationships. To this end, a set of structuring primitives for a dictionary of entity relationship data schemas is presented. The formal properties of such structuring primitives are investigated, and the feasibility of their usage is shown by providing a methodology for dictionary design. >

Hierarchies and planarity theory

In diagrammatic representations of hierarchies the minimization of the number of crossings between edges is a well-known criterion for improving readability. An efficient algorithm for testing if a hierarchy is planar (i.e. if it can be drawn without edge crossings) is proposed. A complete combinatorial characterization of the class of planar hierarchies is also given. >

A framework for dynamic graph drawing

In this paper we give a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing. We present dynamic algorithms for drawing planar graphs that use a variety of drawing standards (such as polyline, straight-line, orthogonal, grid, upward, and visibility drawings), and address aesthetic criteria that are important for readability, such as the display of planarity, symmetry, and reachability. Also, we provide techniques that are especially tailored for important subclasses of planar graphs such as trees and series-parallel digraphs. Our dynamic drawing algorithms have the important property of performing “smooth updates” of the drawing. Of special geometric interest is the possibility of performing point-location and window queries on the implicit representation of the drawing.

Area requirement and symmetry display in drawing graphs

A classical result shows that every planar graph admits a planar drawing with straight-line edges (struight-line druwing) [S, 25,26,34]. However, the existence of planar straight-line drawings with vertices placed at grid points (i.e., with integer coordinates) and polynomial area has been one of the most important and intriguing open problems in this field [23]. This question has been positively settled by de Fraysseix, Path and Pollack [9], and, independently, by Schnyder [24], who show that every n-vertex planar graph admits a planar straight-line drawing with vertices placed at grid points and 0 (n2) area.

Automatic layout of PERT diagrams with X-PERT

Techniques for visualizing PERT diagrams are presented. These techniques are used in the graphics tool X-PERT for computer-aided development and analysis of PERT diagrams, which provides an integrated environment to construct, display, and analyze PERT diagrams. Several graphics standards are supported, allowing for various styles of vertices (circles, boxes, etc.) and edges (straight lines, polygonal lines, horizontal and vertical segments, etc.).<<ETX>>