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...

Given a rectilinear domain P of h pairwise-disjoint rectilinear obstacles with a total of n vertices in the plane, we study the problem of computing bicriteria rectilinear shortest paths between two points s and t in P. Three types of bicriteria rectilinear paths are considered: minimum-link shortest paths, shortest minimum-link paths, and minimum-cost paths where the cost of a path is a non-de...

We consider a setting where we are given a graph G = (R, E), where R = {R1, . . . , Rn} is a set of polygonal regions in the plane. Placing a point pi inside each region Ri turns G into an edge-weighted graph Gp , p = {p1, . . . , pn}, where the cost of (Ri, Rj) ∈ E is the distance between pi and pj . The Shortest Path Problem with Neighborhoods asks, for given Rs and Rt, to find a placement p ...

The fastest exact algorithm (in practice) for the rectilinear Steiner tree problem in the plane uses a two-phase scheme: First a small but suucient set of full Steiner trees (FSTs) is generated and then a Steiner minimum tree is constructed from this set by using simple backtrack search, dynamic programming or an integer programming formulation. FST generation methods can be seen as problem red...

Let P be a simple rectilinear polygon with n vertices, endowed with rectilinear metric. Let us assign to points Xl,..., xk E P positive weights ~1, . . . , wk. The median problem consists in the computing the point minimizing the total weighted distances to the given points. We present an 0 (n + k log n ) algorithm for solving this median problem. If all weighted points are vertices of a polygo...

We present a fast algorithm to compute an optimal rec-tilinear Steiner tree for extremal point sets. A point set is extremal if each point lies on the boundary of a rectilinear convex hull of the point set. Our algorithm can be used in homotopic routing in VLSI layout design and it runs in O(k 2 n) time, where n is the size of the point set and k is the size of its rectilinear convex hull.

The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...