Portal de Periódicos da CAPES

Fast and compact planar embeddings

2020; Elsevier BV; Volume: 89; Linguagem: Inglês

10.1016/j.comgeo.2020.101630

1879-081X

Leo Ferres, José Fuentes‐Sepúlveda, Travis Gagie, Meng He, Gonzalo Navarro,

DNA and Biological Computing

There are many representations of planar graphs, but few are as elegant as Turán'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 Turán'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.