Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Jain, Naman
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403785871