Abstract
A polynomial-time algorithm for testing if a triconnected directed graph has an upward drkwing is presented. An upward drkwing is a planar drkwing such that all the edges flow in a common direction (e.g., from bottom to top). The problem arises in the fields of automatic graph drkwing and ordered sets, and has been open for several years. The proposed algorithm is based on a new combinatorial characterization that maps the problem into a max-flow problem on a sparse network; the time complexity isO(n+r 2), wheren is the number of vertices andr is the number of sources and sinks of the directed graph. If the directed graph has an upward drkwing, the algorithm allows us to construct one easily.
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Communicated by Takao Nishizeki.
This work was partially supported by the Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of the Italian National Research Council (CNR) Sottoprogetto 6, Infokit and by the ESPRIT II Basic Research Actions Program of the EC (project ALgorithms and COMplexity). An extended abstract of this paper has been presented in P. Bertolazzi and G. Di Battista, “On Upward Drkwing Testing of Triconnected Digraphs,”Proc. 7th ACM Symposium on Computational Geometry, pp. 272–280, 1991.
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Bertolazzi, P., Battista, G.D., Liotta, G. et al. Upward drawings of triconnected digraphs. Algorithmica 12, 476–497 (1994). https://doi.org/10.1007/BF01188716
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DOI: https://doi.org/10.1007/BF01188716