In this paper we give an optimal O(n log n) time and O(n) space algorithm to compute the rectilinear convex layers of a set S of n points on the plane. We also compute the rotation of S that minimizes the number of rectilinear convex layers in O(n log n) time and O(n) space.

Given a simple rectilinear polygon P with k sides and n terminals on its boundary, we present an O(k 3 n)-time algorithm to compute the minimal rectilinear Steiner tree lying inside P interconnecting the terminals. We obtain our result by proving structural properties of a selective set of minimal Steiner trees and exploiting them in a dynamic programming algorithm.

The Steiner tree problem requires to nd a shortest tree connecting a given set of terminal points in a metric space. We suggest a better and fast heuristic for the Steiner problem in graphs and in rectilinear plane. This heuristic nds a Steiner tree at most 1.757 and 1.267 times longer than the optimal solution in graphs and rectilinear plane, respectively.

We propose variable rectilinear interpolation (VRI) as an alternative method for device characterization. Based on a rectilinear structure, this algorithm constructs a mapping with non-uniform nodes placed to maximize informational entropy while meeting the pre-defined error tolerance threshold. In this paper we describe the VRI algorithm and structure; followed by an example in which we charac...

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter...

Routing is a phase in the physical design of Electronic Circuits. The main aim of routing in VLSI design is to interconnect the cells that have been assigned positions as a solution of the placement problem. The problem of finding Rectilinear SteinerMinimal Tree (RSMT) is one of the fundamental problems in the field of Electronic Design Automation. The obstacle avoiding rectilinear Steiner mini...

In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algo...

The embedding problem for a class of graphs called rectilinear graphs is discussed. These graphs have applications in many VLSI Layout Problems. An interesting topological characterization of these graphs lead to efficient algorithms for recognizing and embedding rectilinear graphs which are embeddable on the plane.

BACKGROUND AND PURPOSE MR imaging of moving patients can be challenging and motion correction techniques have been proposed though some have associated new artifacts. The objective of this study was to semiquantitatively compare brain MR images of moving patients obtained at 1.5T by using partially radial and rectilinear acquisition techniques. MATERIALS AND METHODS FLAIR, T2-, T1-, and contr...