In this paper, an O ( n log log n ) algorithm is proposed for minimally rectangular partitioning a simple rectilinear polygon. For any simple rectilinear polygon P , a vertex-edge visible pair is a vertex and an edge that can be connected by a horizontal or vertical line segment that lies entirely inside P . We show that, if the vertex-edge visible pairs are found, the maximum matching and the ...

In a rectilinear drawing of a simple graph G each vertex is mapped to a distinct point in the plane and each edge is represented by a straight-line segment with appropriate ends. The goal of rectilinear crossing minimization is to find a rectilinear drawing of G with as few edge crossings as possible. A new approach to rectilinear crossing minimization is presented including a formulation of th...

Spatial joins are very important but costly operations in spatial databases. A typical evaluation strategy of spatial joins is to perform the join on approximations of spatial objects and then evaluate the join of the real objects based on the results. The common approximation is the minimum bounding rectangle. Minimum bounding rectangles are coarse approximations of spatial objects and may cau...

A rectilinear Steiner tree for a set T of points in the plane is a tree which connects T using horizontal and vertical lines, In the Rectilinear Steiner Tree problem, input is a set T of n points in the Euclidean plane (R) and the goal is to find an rectilinear Steiner tree for T of smallest possible total length. A rectilinear Steiner arborecence for a set T of points and root r ∈ T is a recti...

A path or a polygonal domain is C-oriented if the orientations of its edges belong to a set of C given orientations; this is a generalization of the notable rectilinear case (C = 2). We study exact and approximation algorithms for minimum-link C-oriented paths and paths with unrestricted orientations, both in C-oriented and in general domains. We obtain the following results: • An optimal algor...