Spirality and Rectilinear Planarity Testing of Independent-Parallel SP-Graphs
Abstract
We study the long-standing open problem of efficiently testing rectilinear planarity of series-parallel graphs (SP-graphs) in the variable embedding setting. A key ingredient behind the design of a linear-time testing algorithm for SP-graphs of vertex-degree at most three is that one can restrict the attention to a constant number of ``rectilinear shapes'' for each series or parallel component. To formally describe these shapes the notion of spirality can be used. This key ingredient no longer holds for SP-graphs with vertices of degree four, as we prove a logarithmic lower bound on the spirality of their components. The bound holds even for the independent-parallel SP-graphs, in which no two parallel components share a pole. Nonetheless, by studying the spirality properties of the independent-parallel SP-graphs, we are able to design a linear-time rectilinear planarity testing algorithm for this graph family.
Keywords
Cite
@article{arxiv.2110.00548,
title = {Spirality and Rectilinear Planarity Testing of Independent-Parallel SP-Graphs},
author = {Walter Didimo and Michael Kaufmann and Giuseppe Liotta and Giacomo Ortali},
journal= {arXiv preprint arXiv:2110.00548},
year = {2021}
}