Fast and Compact Planar Embeddings

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)


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.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversidad del DesarrolloConcepciónChile
  2. 2.CeBiB; Department of Computer ScienceUniversity of ChileSantiagoChile
  3. 3.CeBiB; EITDiego Portales UniversitySantiagoChile
  4. 4.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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