Computing Labeled Orthogonal Drawings
This paper studies the problem of computing labeled orthogonal drawings. A label is modeled as a rectangle of prescribed size and it can be associated with either a vertex or an edge. Several optimization goals are taken into account. Namely, the labeled drawing can be required to have minimum total edge length, minimum width, minimum height, or minimum area. We present ILP models to compute optimal drawings with respect to the first three objectives and an algorithm exploiting these models which computes a drawing of minimum area (the compaction problem is known to be NP-complete in general).
- 1.C. Binucci, W. Didimo, G. Liotta, and M. Nonato. Computing labeled orthogonal drawings, manuscript: http://www.diei.unipg.it/PAG PERS/binucci/binucci.htm.
- 2.C. Binucci, W. Didimo, G. Liotta, and M. Nonato. Labeling heuristics for orthogonal drawings. In Symposium on Graph Drawing (GD’01), volume 2265 of LNCS, pages 139–153, 2002.Google Scholar
- 4.R. Castello, R. Milli, and I. Tollis. An algorithmic framework for visualizing statecharts. In Symposium on Graph Drawing (GD’00), volume 1984 of LNCS, pages 139–149, 2001.Google Scholar
- 5.G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing. Prentice Hall, Upper Saddle River, NJ, 1999.Google Scholar
- 7.K. G. Kakoulis and I. G. Tollis. An algorithm for labeling edges of hierarchical drawings. In Symposium on Graph Drawing (GD’97), volume 1353 of LNCS, pages 169–180, 1998.Google Scholar
- 9.M. Kaufmann and D. Wagner. Drawing Graphs. Springer Verlag, 2001.Google Scholar
- 10.G. Klau and P. Mutzel. Optimal labeling of point features in rectangular labeling models. Mathematical Programming, Series B, To appear.Google Scholar
- 11.G. Klau and P. Mutzel. Combining graph labeling and compaction. In Symposium on Graph Drawing (GD’99), LNCS, pages 27–37, 1999.Google Scholar
- 13.G. Klau and P. Mutzel. Optimal labelling of point features in the sliding model. In In Proc. COCOON’00, volume 1858 of LNCS, pages 340–350, 2001.Google Scholar
- 14.S. Nakano, T. Nishizeki, T. Tokuyama, and S. Watanabe. Labeling points with rectangles of various shape. In Symposium on Graph Drawing (GD’00), volume 1984 of LNCS, pages 91–102, 2001.Google Scholar
- 15.T. Nishizeki and N. Chiba. Planar Graphs: Theory and Algorithms, volume 32 of Annals of Discrete Mathematics. North-Holland, 1988.Google Scholar
- 17.T. Strijk and A. Wol.. The map labeling bibliography. on-line: http://www.mathinf. uni-greifswald.de/map-labeling/bibliography/.