Roberto Tamassia

Algorithms for drawing graphs: an annotated bibliography

Several data presentation problems involve drawing graphs so that they are easy to read and understand. Examples include circuit schematics and diagrams for information systems analysis and design. In this paper we present a bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs. Research on this topic is spread over the broad spectrum of computer science. This bibliography constitutes a first attempt to encompass both theoretical and application-oriented papers from disparate areas.

On embedding a graph in the grid with the minimum number of bends

Given a planar graph G together with a planar representation P, a region preserving grid embedding of G is a planar embedding of G in the rectilinear grid that has planar representation isomorphic to P. In this paper, an algorithm is presented that computes a region preserving grid embedding with the minimum number of bends in edges. This algorithm makes use of network flow techniques, and runs in time

Automatic graph drawing and readability of diagrams

O(n^2 \log n)

A unified approach to visibility representations of planar graphs

, where n is the number of vertices of the graph. Constrained versions of the problem are also considered, and most results are extended to k-gonal graphs, i.e., graphs whose edges are sequences of segments with slope multiple of

On the Computational Complexity of Upward and Rectilinear Planarity Testing

{{180} / k}

Algorithms for plane representations of acyclic digraphs

degrees. Applications of the above results can be found in several areas: VLSI circuit layout, architectural design, communication by light or microwave, transportation problems, and automatic layout of graphlike diagrams.

On-Line Planarity Testing

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. >

Efficient Tree-Based Revocation in Groups of Low-State Devices

We studyvisibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments that intersect only adjacent vertex-segments. Every graph that admits this representation must be planar. We consider three types of visibility representations, and we give complete characterizations of the classes of graphs that admit them. Furthermore, we present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs. Many applications of our results can be found in VLSI layout.

Implementation of an authenticated dictionary with skip lists and commutative hashing

A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment and no two edges cross. Testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures. For example, upward planarity is useful for the display of order diagrams and subroutine-call graphs, while rectilinear planarity is useful for the display of circuit schematics and entity-relationship diagrams. We show that upward planarity testing and rectilinear planarity testing are NP-complete problems. We also show that it is NP-hard to approximate the minimum number of bends in a planar orthogonal drawing of an n-vertex graph with an

Dynamic algorithms in computational geometry

O(n^{1-\epsilon})