Algorithms for visibility representations of planar graphs
We investigate visibility representations of planar graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments that intersect only adjacent vertex-segments. We consider three types of visibility representations, and present linear time algorithms for testing the existence of and constructing visibility representations. Applications of our results can be found in VLSI layout compaction, and in efficient embedding of graphs in the rectilinear grid.
Unable to display preview. Download preview PDF.
- P. Duchet, Y. Hamidoune, M. Las Vergnas, and H. Meyniel, “Representing a Planar Graph by Vertical Lines Joining Different Levels,” Discrete Mathematics, vol. 46, pp. 319–321, 1983.Google Scholar
- S. Even, Graph Algorithms, Computer Science Press, 1979.Google Scholar
- J. Hopcroft and R. Tarjan, “Efficient Planarity Testing,” J. of ACM, vol. 21, no. 4, pp. 549–568, 1974.Google Scholar
- A. Lempel, S. Even, and I. Cederbaum, “An Algorithm for Planarity Testing of Graphs,” Theory of Graphs, International Symposium, Rome, pp. 215–232, 1966.Google Scholar
- F. Luccio, S. Mazzone, and C.K. Wong, “A Note on Visibility Graphos,” Manuscript, Pisa, 1983.Google Scholar
- L.A. Melnikov, Problem at the 6th Hungarian Colloquium on Combinatorics, 1981.Google Scholar
- R.H.J.M. Otten and J.G. van Wijk, “Graph Representations in Interactive Layout Design,” Proc. IEEE Int. Symposium on Circuits and Systems, New York, pp. 914–918, 1978.Google Scholar
- M. Schlag, F. Luccio, P. Maestrini, D.T. Lee, and C.K. Wong, “A Visibility Problem in VLSI Layout Compaction,” pp. 259–282 in Advances in Computing Research, vol. 2, ed. F.P. Preparata. JAI Press Inc., 1985.Google Scholar
- J.A. Storer, “On minimal node-cost planar embeddings,” Networks, vol. 14, pp. 181–212, 1984.Google Scholar
- R. Tamassia and I.G. Tollis, “A Provably Good Linear Algorithm for Embedding Graphs in the Rectilinear Grid,” Manuscript, Urbana, May 1985.Google Scholar
- R. Tamassia and I.G. Tollis, “Plane representations of graphs and visibility between parallel segments,” Technical Report ACT-57, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, April 1985.Google Scholar
- C. Thomassen, “Plane Representations of Graphs,” pp. 43–69 in Progress in Graph Theory, ed. J.A. Bondy and U.S.R. Murty, Academic Press, 1984.Google Scholar
- S.K. Wismath, “Characterizing bar line-of-sight graphs,” Proc. of ACM Symposium on Computational Geometry, Baltimore, Maryland, pp. 147–152, June 1985.Google Scholar