We present linear-time algorithms to construct tree-like Voronoi diagrams with disconnected regions after the sequence of their faces along an enclosing boundary (or at infinity) is known. We focus on the farthest-segment Voronoi diagram, however, our techniques are also applicable to constructing the order-(k+1) subdivision within an order-k Voronoi region of segments and updating a nearest-ne...

For any two points in a simple polygon P , the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regi...

The traditional K-means clustering algorithm is difficult to initialize the number of clusters K, and the initial cluster centers are selected randomly, this makes the clustering results very unstable. Meanwhile, algorithms are susceptible to noise points. To solve the problems, the traditional K-means algorithm is improved. The improved method is divided into the same grid in space, according ...

Pareto-optimal objects are favored as each of such objects has at least one competitive edge against all other objects, or “not dominated.” Recently, in the database literature, skyline queries have gained attention as an effective way to identify such pareto-optimal objects. In particular, this paper studies the pareto-optimal objects in perspective of facility or business locations. More spec...

The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restr...

In this paper, the computation of positiveα-hull for a set of planar closedC-continuous curves has been addressed without sampling the curves into point-sets or polylines. Positive α-hull, so far, has been computed only for a set of points, using the farthest Delaunay triangulation, a dual of farthest Voronoi diagram. However, Delaunay triangulation does not exist for a set of curved boundaries...

We investigate the higher-order Voronoi diagrams of n point sites with respect to the geodesic distance in a simple polygon with h > 0 polygonal holes and c corners. Given a set of n point sites, the korder Voronoi diagram partitions the plane into several regions such that all points in a region share the same k nearest sites. The nearest-site (first-order) geodesic Voronoi diagram has already...

The construction of a minimum-width annulus of a set of objects in the plane has useful applications in diverse fields, such as tolerancing metrology and facility location. We present a novel implementation of an algorithm for obtaining a minimum-width annulus containing a given set of disks in the plane, in case one exists. The algorithm extends previously known methods for constructing minimu...

Sparse representation based classification (SRC) has achieved state-of-the-art results on face recognition. It is hence desired to extend its power to a broader range of classification tasks in pattern recognition. SRC first encodes a query sample as a linear combination of a few atoms from a predefined dictionary. It then identifies the label by evaluating which class results in the minimum re...

We reflect upon an analogue of the cut locus, a notion classically studied in Differential Geometry, for finite graphs. The cut locus C(x) of a vertex x shall be the graph induced by the set of all vertices y with the property that no shortest path between x and z, z 6= y, contains y. The cut locus coincides with the graph induced by the vertices realizing the local maxima of the distance funct...