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...

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...

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 ...

The unsteady flow of a visco-elastic Maxwell fluid through a rectilinear pipe having its cross-section as a parallelogram under the influence of a axial pressure gradient (I) varying linearly with time , and (II) decreasing exponentially with time has been discussed in the present paper. Variables separable and Laplace transform methods have been used to solve the problem.