Large planar Poisson–Voronoi cells containing a given convex body

Finding Large Planar Subgraphs and Large Subgraphs of a Given Genus

We consider the MAXIMUM PLANAR SUBGRAPH problem given a graph G, nd a largest planar subgraph of G. This problem has applications in circuit layout, facility layout, and graph drawing. We improve to 4/9 the best known approximation ratio for the MAXIMUM PLANAR SUBGRAPH problem. We also consider a generalization of the previous problem, the MAXIMUM GENUS D SUBGRAPH problem-given a connected grap...

Is There a Planar Convex Set with Given Width, Diameter, and Inradius?

Finding Meaningful Regions Containing Given Keywords from Large Text Collections

Introduction When we search a large text collection for documents we want, we will specify some keywords and we obtain documents containing the keywords. Because the search result contains many documents, it is important to rank them. Though some methods are proposed for ranking, they did not consider positions of the keywords. As a result, such documents sometimes may be useless because the ke...

Planar Point Sets With Large Minimum Convex Decompositions

We show the existence of sets with n points (n > 4) for which every convex decomposition contains more than f§« — § polygons, which refutes the conjecture that for every set of n points there is a convex decomposition with at most n + C polygons. For sets having exactly three extreme points we show that more than n + s/2(n 3) 4 polygons may be necessary to form a convex decomposition.

Dynamic Planar Convex Hull

In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(logn) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangen...