Parallel Graph Drawing Algorithm for Bipartite Planar Graphs

TL;DR

A parallel algorithm for st-numbering which uses an ear decomposition search to assign vertical and horizontal segments to the vertices of any planar bipartite graph in the following manner: i) Two segments cannot share an interior point ii) Two segments intersect if and only if the corresponding vertices are adjacent.

Abstract

We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two segments intersect if and only if the corresponding vertices are adjacent, which uses a polynomial number of processors. In other words, represent vertices of a planar bipartite graph as parallel segments, and edges as intersection points between these segments. Note that two segments are not allowed to cross. Our method is based on a parallel algorithm for st-numbering which uses an ear decomposition search.

Figures (2)

• Figure 1: An image showing the corrected pointers from each point $u_k$
• Figure 2: An image showing the graph with new edges added