Angular resolution of straight-line drawings (abstract)

Abstract

An orthogonal drawing of a graph is such that the edges are represented by polygonal chains consisting of horizontal and vertical segments. The intermediate vertices of the chain (which are not vertices of the graph) are called bends. In this talk we survey algorithms for constructing planar orthogonal drawings. The main quality measures considered are the minimization of the number of bends and of the area of the drawing. The construction of planar orthogonal drawings has many important applications, including graph visualization, VLSI layout, facilities floorplanning, and communication by light or microwave. Given an embedded planar graph G with n vertices, a planar orthogonal drawing of G with the minimum number of bends can be computed in O ( n 2 log n ) time using network-flow techniques. Drawings with O (n) bends can be constructed in O (n) time using visibility representations. Also, there are families of graphs that require Ω (n) bends. Open problems include minimizing bends over all possible embeddings, and finding an efficient parallel algorithm for bend minimization.