Nice drawings for planar bipartite graphs
Graph drawing algorithms usually attempt to display the characteristic properties of the input graphs. In this paper we consider the class of planar bipartite graphs and try to achieve planar drawings such that the bipartiteness property is cleary shown. To this aim, we develop several models, give efficient algorithms to find a corresponding drawing if possible or prove the hardness of the problem.
Unable to display preview. Download preview PDF.
- Di Battista G., P. Eades, R. Tamassia and I.G. Tollis, ‘Algorithms for Drawing Graphs: an Annotated Bibliography', Computational Geometry: Theory & Applications, (1994), pp. 235–282.Google Scholar
- Di Battista G., W.-P. Liu and I. Rival, ‘Bipartite graphs, upward drawings, and planarity', Information Processing Letters, 36 (1990), pp. 317–322.Google Scholar
- Eades P., ‘A heuristic for graph drawing', Congr. Numerant., (1984), pp. 149–160.Google Scholar
- Eades P., B.D. McKay and N. Wormald, ‘On an edge crossing problem', Proc. Australian Computer Science Conf., Austr. Nat. Univ. (1986), pp. 327–334.Google Scholar
- Eades P. and N. Wormald, ‘The Median Heuristic for Drawing 2-layered Networks', Technical Report 69, Dept. of Comp. Science, Univ. of Queensland, 1986.Google Scholar
- Fraysseix, H. de, J. Pach and R. Pollack, ‘How to draw a planar graph on a grid', Combinatorica 10 (1990), pp. 41–51.Google Scholar
- Garey, M.R. and D.S. Johnson, ‘Crossing Number is NP-complete', SIAM J. Algebraic and Discrete Methods, 4(3) (1983), pp. 312–316.Google Scholar
- Garey, M.R., D.S. Johnson and R.E. Tarjan, ‘The Planar Hamiltonian Circuit Problem is NP-complete', SIAM J. Comput. 5 (1976), pp. 704–714.Google Scholar
- Jünger M. and P. Mutzel, 'Exact and Heuristic Algorithms for 2-Layer Straightline Crossing Minimization', Proc. Graph Drawing, (1995), LNCS 1027, pp. 337–349.Google Scholar
- Mitchell S.L. ‘Linear algorithms to recognize outerplanar and maximal outplanar graphs', Information Processing Letters 9 (1979), pp. 229–232.Google Scholar
- Kamada T. and S. Kawai, ‘An algorithm for drawing general undirected graphs', Information Processing Letters, 31 (1989), pp. 70–15.Google Scholar
- Sugiyama K., S. Tagawa and M. Toda, ‘Methods for visual understanding of hierarchical Systems', IEEE Trans. on Systems, Man and Cybern., 11 (1981), pp.109–125.Google Scholar
- Tomii, N., Y. Kambayashi, and Y. Shuzo, ‘On Planarization Algorithms of 2-Level Graphs', Papers of tech. group on elect. comp., IECEJ, EC77-38 (1977), pp. 1–12.Google Scholar