Titlebook: ;

Gesture

Geometric Thickness of Complete Graphsdge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantities, the (graph-theoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, ... We show that the geometric thick

octogenarian

Balanced Aspect Ratio Trees and Their Use for Drawing Very Large Graphs introduce a novel BSP-type decomposition, called the . (BAR) tree, which guarantees that the cells produced are convex and have bounded aspect ratios. In addition, the tree depth is .(log.), and its construction takes .(. log .) time, where . is the number of points. We show that the BAR tree can b

敲竹杠

On Improving Orthogonal Drawings: The 4M-Algorithme algorithms lead to unpleasant drawings with many bends and a large area. We present methods how to improve the quality of given orthogonal drawings. Our algorithms try to simulate the thinking of a human spectator in order to achieve good results. We also give instructions how to implement the str

商议

擦掉

A Framework for Drawing Planar Graphs with Curves and Polylinesudes several visual properties of such drawings, including aspect ratio, vertex resolution, edge length, edge separation, and edge curvature, as well as complexity measures such as vertex and edge representational complexity and the area of the drawing. In addition to this general framework, we pres

faucet

Planar Polyline Drawings with Good Angular Resolution) × (3/2. − 7/2) grid with at most 5. − 15 bends and minimum angle > 2/.. In the constructed drawings, every edge has at most three bends and length .(.). To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the grid size, angular resolution, and number of bends for

DEFER

A Layout Adjustment Problem for Disjoint Rectangles Preserving Orthogonal Order of the rectangles and preserves the orthogonal order. Misue et al. proposed an .(..)-time heuristic algorithm for the problem. We first show that the corresponding decision problem for this problem is NP-complete. We also present an .(..)-time heuristic algorithm for the problem that finds a layout

思考而得

Drawing Algorithms for Series-Parallel Digraphs in Two and Three Dimensions, the other constructs three dimensional drawings with a footprint of minimum size..Future work will include combinations of these two algorithms: we would like to display as much symmetry as possible in a three dimensional drawing of small footprint.

hematuria

rectum

Level Planarity Testing in Linear Timeh . ∈ .. and . ∈ .. we have . <.. The level planarity testing problem is to decide if . can be drawn in the plane such that for each level .., all . ∈ .. are drawn on the line .. = (., . − .) ∣. ∈ ℝ , the edges are drawn monotone with respect to the vertical direction, and no edges intersect except