A graph is rectilinear planar if it admits a orthogonal drawing without bends. While testing planarity NP-hard in general, long-standing open problem to establish tight upper bound on its complexity for partial 2-trees, i.e., graphs whose biconnected components are series-parallel. We describe new $$O(n^2 \log ^2 n)$$ -time algorithm test of which improves over the current best $$O(n^3 . Moreov...

This paper presents an algorithm for converting the contour of a 2D workpiece into a rectilinear polygon. The purpose of providing such a conversion is to mode1 the global shape information of the workpiece. Using an existing algorithm, the rectilinear polygon can further be modeled by a tree structure of line segments, known as the simplified skeleton, which can concisely model the global shap...

We present a data structure that allows to preprocess a rectilinear polygon with n vertices such that, for any two query points, the shortest path in the rectilinear link or L 1-metric can be reported in time O(log n + k) where k is the link length of the shortest path. If only the distance is of interest, the query time reduces to O(log n). Furthermore, if the query points are two vertices, th...

The rectilinear Steiner tree problem i s t o find a manimum-length set of horizontal and vertical line segments that interconnect a given set of points in $he plane. Here we study the thumbnail rectilinear S te iner tree problem, where the inpvt points are drawn f r o m a small integer grid. Specifically, we devise a full-set decomposition algorithm for computing opt ima l thumbnail rectalinear...

Given a signal net N = s; 1; ;n to be the set of nodes, with s the source and the remaining nodes sinks, an MRDPT (minimum-cost rectilinear Steiner distance-preserving tree) has the property that the length of every source to sink path is equal to the rectilinear distance between the source and sink. The minimum-cost rectilinear Steiner distance-preserving tree minimizes the total wire length w...

The digital autofluoroscope is a scintillation cam era with a 15.2 X 22.9-cm rectangular array of 294 sodium iodide crystals. Since the development of the digital autofluoro scope by Bender and Blau in 1960 (/). it has been used for static imaging and dynamic studies of vari ous organs of the body (2-5). The Baird-Atomic model 5600 digital autofluoroscope had been used for static brain imaging ...

*Prepared in the Program Division, B u reau of Employment Security. D U R I N G 1946, employers subject to State unemployment insurance laws were taxed at an estimated average rate of 1.4 percent of taxable pay rolls (table l ) 1 —the lowest average rate since the first year of the program (1936) when the Federal tax rate was only 1 percent. The 1.4percent revenue rate is expected to yield $828...

The restriction of Pipe, a potential glycosaminoglycan-modifying enzyme, to ventral follicle cells of the egg chamber is essential for dorsoventral axis formation in the Drosophila embryo. pipe repression depends on the TGFalpha-like ligand Gurken, which activates the Drosophila EGF receptor in dorsal follicle cells. An analysis of Raf mutant clones shows that EGF signalling is required cell-au...