1 SUMMARY This paper is concerned with the application of radial basis function networks (RBFNs) for solving non-Newtonian fluid flow problems. Indirect RBFNs, which are based on an integration process, are employed to represent the solution variables; the governing differential equations are discretized by means of point collocation. To enhance numerical stability, stress-splitting techniques ...

This paper presents new heuristic algorithms using the guided A* search method : Guided Minimum Detour (GMD) algorithm and Line-by-Line Guided Minimum Detour (LGMD) algorithm for finding optimal rectilinear (L,) shortest paths in the presence of rectilinear obstacles. The GMD algorithm runs O(nhr(1ogN) + tN) in time and takes O(N) in space, where N is the number of extended line segments includ...

We establish tight bounds for beacon-based coverage problems, and improve the bounds for beacon-based routing problems in simple rectilinear polygons. Specifically, we show that bn6 c beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. We also prove tight bounds for the case where P is monotone, and we present an optimal linear-time alg...

In this paper, we consider the problem of computing, for a given rectilinear angle sequence, a “small” rectilinear polygon. A rectilinear angle sequence S is a sequence of left (90◦) turns and right (270◦) turns, that is, S = (s1, . . . , sn) ∈ {L, R}, where n is the length of S. As we consider only rectilinear angle sequences, we usually drop the term “rectilinear.” A polygon P realizes an ang...

We consider a generalization of the Rectilinear Steiner Tree problem, where our input is classes of required points instead of simple required points. Our task is to nd a minimum rectilinear tree connecting at least one point from each class. We prove that the version, where all required points lie on two parallel lines, called the Recti-linear Class Steiner Tree (channel) problem, is NP-hard. ...

We present an algorithm for computing k-link rectilinear shortest paths among rectilinear obstacles in the plane. We extend the “continuous Dijkstra” paradigm to store the link distance information associated with each propagating “wavefront”. Our algorithm runs in time O(kn log n) and space O(kn), where n is the number of vertices of the obstacles. Previous algorithms for the problem had worst...