Bend to Open?

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

To bend or not to bend are heteroatom interactions within conjugated molecules effective in dictating conformation and planarity?

We consider the roles of heteroatoms (mainly nitrogen, the halogens and the chalcogens) in dictating the conformation of linear conjugated molecules and polymers through non-covalent intramolecular interactions. Whilst hydrogen bonding is a competitive and sometimes more influential interaction, we provide unambiguous evidence that heteroatoms are able to determine the conformation of such mate...

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...

Accelerated Bend Minimization

We present an O(n) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n7/4√logn) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated min-cost flow problem on a planar bidirected graph with bounded c...

Bend into shape

Bacteria come in a variety of shapes, as most species elaborate on the ‘default’ sphere to resemble ovoids, rods, bend rods, spirals, branched filaments or other more complicated forms. How cells that are under considerable turgor pressure maintain a nonspherical shape is unclear, though it is known to depend on structural elements on either side of the cytoplasmic membrane: the murein (peptido...