We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set P of h pairwise-disjoint rectilinear polygonal obstacles with a total of n vertices in the plane, a minimumlink rectilinear path between two points is a rectilinear path that avoids all obstacles with ...

Problem statement: The objective of this study is to develop efficient exact algorithms for a single source capacitated multi-facility location problem with rectilinear distance. This problem is concerned with locating m capacitated facilities in the two dimensional plane to satisfy the demand of n customers with minimum total transportation cost which is proportional to the rectilinear distanc...

Scheinerman and Wilf [SW94] assert that “an important open problem in the study of graph embeddings is to determine the rectilinear crossing number of the complete graph Kn.” A rectilinear drawing of Kn is an arrangement of n vertices in the plane, every pair of which is connected by an edge that is a line segment. We assume that no three vertices are collinear, and that no three edges intersec...

We present a general rectilinear Steiner tree problem in the plane and prove that it is solvable on the Hanan grid of the input points. This result is then used to show that several variants of the ordinary rectilinear Steiner tree problem are solvable on the Hanan grid, including | but not limited to | Steiner trees for rectilinear (or iso-thetic) polygons, obstacle-avoiding Steiner trees, gro...

The author surveys methods for finding a path between two arbitrary points within a 2D polygon under the link-distance metric. Early algorithms limited to simple polygons are explored first, and categorized into two different approaches. These methods are then evaluated for expansion into non-simple polygons (i.e. spaces with “Obstacles” within the polygon boundary). Then, the problem of findin...

In this paper, a three-layer force-directed self-organizing map is designed to resolve the circuit placement problem with arbitrarily shaped rectilinear modules. The proposed neural model with an additional hidden layer can easily model a rectilinear module by a set of hidden neurons to correspond the partitioned rectangles. With the collective computing from hidden neurons, these rectilinear m...

This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the Rectilinear Line Cover where the inputs are n points in R and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines where these lines are restricted to be axis parallel. We show that this problem has efficie...

The problem of constructing an optimal Steiner tree is NP-complete. Mapping the problem to standard Cartesian coordinates, the cost of an optimal Steiner tree is defined as the minimal rectilinear distance of all the edges. The heuristic proposed in this paper then finds a close approximation in fast (polynomial) time. The basis of exploits the idea of triangular distance, that is, using distan...