Fast and Compact Planar Embeddings
Abstract
There are many representations of planar graphs, but few are as elegant as Tur\'an's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main disadvantage has been that "it does not allow efficient searching" (Jacobson, 1989). In this paper we show how to add a sublinear number of bits to Tur\'an's representation such that it supports fast navigation while retaining simplicity. As a consequence of the inherited simplicity, we offer the first efficient parallel construction of a compact encoding of a planar graph embedding. Our experimental results show that the resulting representation uses about 6 bits per edge in practice, supports basic navigation operations within a few microseconds, and can be built sequentially at a rate below 1 microsecond per edge, featuring a linear speedup with a parallel efficiency around 50\% for large datasets.
Keywords
Cite
@article{arxiv.1610.00130,
title = {Fast and Compact Planar Embeddings},
author = {Leo Ferres and José Fuentes and Travis Gagie and Meng He and Gonzalo Navarro},
journal= {arXiv preprint arXiv:1610.00130},
year = {2018}
}
Comments
This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941. Conference version presented at WADS 2017