We prove the following graph coloring result Let G be a connected bipartite planar graph Then one can triangulate G in such a way that the resulting graph is colorable This result implies several new upper bounds for guarding problems including the rst non trivial upper bound for the rectilinear Prison Yard Problem n vertex guards are su cient to watch the interior of a rectilinear polygon with...

In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set P of n (weighted) uncertain points in the plane and each uncertain point has m possible locations each associated with a probability for the point appearing at that location. The goal is to find a point q∗ in the plane which minimizes the maximum expected rectiline...

Let G = (V,E) be a plane triangulated graph where each vertex is assigned a positive weight. A rectilinear dual of G is a partition of a rectangle into |V | simple rectilinear regions, one for each vertex, such that two regions are adjacent if and only if the corresponding vertices are connected by an edge in E. A rectilinear dual is called a cartogram if the area of each region is equal to the...

To the best of our knowledge, this is the first algorithm unifying arbitrary rectilinear block packing and soft block packing. Furthermore, this algorithm handles arbitrary convex or concave rectilinear block packing in the most efficient way compared to other sequence pair-based approaches. At the same time, the algorithm can handle rectangle soft block effectively. The concept of non-redundan...

We present an eecient algorithm to compute an optimal rectilinear Steiner tree for extremal point sets. A point set is extremal if every point in it lies on the boundary of a rectilinear convex hull of the point set. Our algorithm can be used to construct minimum-length connection for multi-terminal nets in homotopic routing in VLSI layout design. The previous best algorithms run in O(k 4 n) ti...

BACKGROUND Recently, a compact cardiopulmonary support (CPS) system designed for quick set-up for example, during emergency cannulation, has been introduced. Traditional rectilinear percutaneous cannulas are standard for remote vascular access with the original design. The present study was designed to assess the potential of performance increase by the introduction of next-generation, self-exp...