Algorithmic graph drawing

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I intend to continue working in the general area of design and analysis of algorithms. My particular focus lies in the field of Graph Drawing, and includes drawings in both 2 and 3 dimensions. Drawings that permit bends, but with low area/volume are one theme of the proposed research, and significant progress has already been demonstrated under a variety of models and constraints, including orthogonal 3D layouts, constrained point sets, directed graphs, etc. Effective drawings of graphs are critical in various disciplines that require the display of large graphical structures -- the field of Graph Drawing is motivated by these visualization and representation problems. There is substantial overlap in this work with the field of Computational Geometry and many of the required tools were developed in geometrical contexts. I maintain a serious parallel interest in computational geometry problems such as visibility, reconstruction, and arrangement graphs. Over the past several years, software packages for research in these areas, and demos have been developed by my students. This practical application of our results represents an important direction of the proposed research