1-Bend 3-D Orthogonal Box-Drawings: Two Open Problems Solved

1-bend 3-D orthogonal drawings: two open problems solved

1-Bend 3-D Orthogonal Box-Drawings: Two Open Problems Solved

This paper studies three-dimensional orthogonal box-drawings where edge-routes have at most one bend. Two open problems for such drawings are: (1) Does every drawing of Kn have volume Ω(n )? (2) Is there a drawing of Kn for which additionally the vertices are represented by cubes with surface O(n)? This paper answers both questions in the negative, and provides related results concerning volume...

Bend-Minimum Orthogonal Drawings of Plane 3-Graphs

In an orthogonal drawing of a plane graph, any edge is drawn as a sequence of line segments, each having either a horizontal or a vertical direction. A bend is a point where an edge changes its direction. A drawing is called a bend-minimum orthogonal drawing if the number of bends is minimum among all orthogonal drawings. This paper presents a linear-time algorithm to find a bend-minimum orthog...

On Bend-Minimized Orthogonal Drawings of Planar 3-Graphs

An orthogonal drawing of a graph is a planar drawing where each edge is drawn as a sequence of horizontal and vertical line segments. Finding a bend-minimized orthogonal drawing of a planar graph of maximum degree 4 is NP-hard. The problem becomes tractable for planar graphs of maximum degree 3, and the fastest known algorithm takes O(n5 logn) time. Whether a faster algorithm exists has been a ...

Bend Minimization in Planar Orthogonal Drawings Using Integer Programming

We consider the problem of minimizing the number of bends in a planar orthogonal graph drawing. While the problem can be solved via network flow for a given planar embedding of a graph G, it is NP-hard if we consider the set of all planar embeddings of G. Our approach for biconnected graphs combines an integer linear programming (ILP) formulation for the set of all embeddings of a planar graph ...