Abstract
There are many representations of planar graphs but few are as elegant as Turán’s (1984): it is simple and practical, uses only four bits per edge, can handle 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, thus overcoming this disadvantage. Other data structures for planar embeddings may be asymptotically faster or smaller but ours is simpler, and that can be a theoretical as well as a practical advantage: e.g., we show how our structure can be built efficiently in parallel.
The second and fifth authors received travel funding from EU grant H2020-MSCA-RISE-2015 BIRDS GA No. 690941. The second, third and fifth authors received funding from Basal Funds FB0001, Conicyt, Chile. The third author received funding from Academy of Finland grant 268324. Early parts of this work were done while the third author was at the University of Helsinki and while the third and fifth authors were visiting the University of A Coruña. Many thanks to Jérémy Barbay, Luca Castelli Aleardi, Arash Farzan, Ian Munro, Pat Nicholson and Julian Shun. The third author is grateful to the late David Gregory for his course on graph theory.
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Ferres, L., Fuentes, J., Gagie, T., He, M., Navarro, G. (2017). Fast and Compact Planar Embeddings. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_33
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DOI: https://doi.org/10.1007/978-3-319-62127-2_33
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