Takeaki Uno

We are given a set S of n points in the Euclidean plane. We assume that S is in general position. A simple polygon P is an empty polygon of S if each vertex of P is a point in S and every point in S is either outside P or a vertex of P. In this paper, we consider the problem of enumerating all the empty polygons of a given point set. To design an efficient enumeration algorithm, we use a reverse search by Avis and Fukuda with child lists. We propose an algorithm that enumerates all the empty polygons of S in O(n² |ϵ(S) |)-time, where ϵ(S) is the set of empty polygons of S. Moreover, by applying the same idea to the problem of enumerating surrounding polygons of a given point set S, we propose an enumeration algorithm that enumerates them in O(n²)-delay, while the known algorithm enumerates in O(n² log n)-delay, where a surrounding polygon of S is a polygon such that each vertex of the polygon is a point in S and every point in S is either inside the polygon or a vertex of the polygon.

Given a set P of n points and an integer k, we wish to place k facilities on points in P so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem, and the set of such k points is called a k-dispersion of P. Note that the 2-dispersion problem corresponds to the computation of the diameter of P. Thus, the k-dispersion problem is a natural generalization of the diameter problem. In this paper, we consider the case of k=3, which is the 3-dispersion problem, when P is in convex position. We present an O(n²)-time algorithm to compute a 3-dispersion of P.

During a disaster, social media can be both a source of help and of danger: Social media has a potential to diffuse rumors, and officials involved in disaster mitigation must react quickly to the spread of rumor on social media. In this paper, we investigate how topic diversity (i.e., homogeneity of opinions in a topic) depends on the truthfulness of a topic (whether it is a rumor or a non-rumor) and how the topic diversity changes in time after a disaster. To do so, we develop a method for quantifying the topic diversity of the tweet data based on text content. The proposed method is based on clustering a tweet graph using Data polishing that automatically determines the number of subtopics. We perform a case study of tweets posted after the East Japan Great Earthquake on March 11, 2011. We find that rumor topics exhibit more homogeneity of opinions in a topic during diffusion than non-rumor topics. Furthermore, we evaluate the performance of our method and demonstrate its improvement on the runtime for data processing over existing methods.