A Parallel Algorithm for Planar Orthogonal Grid Drawings

In this paper we consider the problem of constructing planar orthogonal grid drawings or more simply, layouts of graphs, with the goal of minimizing the number of bends along the edges. We present optimal parallel algorithms that construct graph layouts with On maximum edge length, On 2 area, and at most 2n + 4 bends for biconnected graphs and 2:4n + 2 bends for simply connected graphs. All three of these quality measures for the layouts are optimal in the worst case for biconnected graphs. The algorithm runs on a CREW PRAM in Ologn time with n= logn processors, thus achieving optimal time and processor utilization. Applications include VLSI layout, graph drawing, and wireless communication.

• Type: Journal
• Year: 2000
• Where: PPL
• Authors: Roberto Tamassia, Ioannis G. Tollis, Jeffrey Scott Vitter
• Keywords: Graph Layouts, Maximum Edge Length, Optimal Parallel, PPL 2000