Background: Graph drawing is one of the important techniques for understanding biological regulations in a cell or among cells at the pathway level. Among many available layout al...
Given a 2k-edge-connected undirected graph, we consider to find a minimum cost orientation that yields a k-arc-connected directed graph. This minimum cost k-arc-connected orientat...
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in Rn . It has recently been shown that properties of the centrosymmetric polytope P = AC are ...
The planarization method has proven to be successful in graph drawing. The output, a combinatorial planar embedding of the so-called planarized graph, can be combined with state-o...
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...