Giuseppe Di Battista

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.

Algorithms for plane representations of acyclic digraphs

Abstract Acyclic digraphs are widely used for representing hierarchical structures. Examples include PERT networks, subroutine-call graphs, family trees, organization charts, Hasse diagrams, and ISA hierarchies in knowledge representation diagrams. We investigate the problem of representing acyclic digraphs in the plane in such a way that all edges flow in the same direction, e.g., from the left to the right or from the bottom to the top. Three plane representations are considered: straight drawings, visibility representations, and grid drawings. We provide efficient algorithms that construct these representations with all edges flowing in the same direction. The time complexity is O(n) for visibility representations and grid drawings, and O(n log n) for straight drawings, where n is the number of vertices of the digraph. For covering digraphs of lattices, the complexity of constructing straight drawings is O(n). We also show that the planar digraphs that admit any one of these representations are exactly the subgraphs of planar st-graphs.

On-Line Planarity Testing

The on-line planarity-testing problem consists of performing the following operations on a planar graph

An experimental comparison of four graph drawing algorithms

G

On-line maintenance of triconnected components with SPQR-trees

: (i) testing if a new edge can be added to

Area requirement and symmetry display of planar upward drawings

G

On-line graph algorithms with SPQR-trees

so that the resulting graph is itself planar; (ii) adding vertices and edges such that planarity is preserved. An efficient technique for on-line planarity testing of a graph is presented that uses

Computing the types of the relationships between autonomous systems

O(n)

Output-Sensitive Reporting of Disjoint Paths

space and supports tests and insertions of vertices and edges in

Bipartite graphs, upward drawings, and planarity

O(\log n)