Abstract
We present two linear-time algorithms for computing a regular edge labeling of 4-connected planar triangular graphs. This labeling is used to compute in linear time a rectangular dual of this class of planar graphs. The two algorithms are based on totally different frameworks, and both are conceptually simpler than the previous known algorithm and are of independent interests. The first algorithm is based on edge contraction. The second algorithm is based on the canonical ordering. This ordering can also be used to compute more compact visibility representations for this class of planar graphs.
The work of the first author was supported by the ESPRIT Basic Research Actions program of the EC under contract No. 7141 (project ALCOM II). The work of the second author was supported by National Science Foundation, grant number CCR-9011214.
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© 1994 Springer-Verlag Berlin Heidelberg
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Kant, G., He, X. (1994). Two algorithms for finding rectangular duals of planar graphs. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_69
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DOI: https://doi.org/10.1007/3-540-57899-4_69
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