Reverse Nearest Neighbor Heat Maps: A Tool for Influence Exploration

We study the problem of constructing a reverse nearest neighbor (RNN) heat map by finding the RNN set of every point in a two-dimensional space. Based on the RNN set of a point, we obtain a quantitative influence (i.e., heat) for the point. The heat map provides a global view on the influence distribution in the space, and hence supports exploratory analyses in many applications such as marketing and resource management. To construct such a heat map, we first reduce it to a problem called Region Coloring (RC), which divides the space into disjoint regions within which all the points have the same RNN set. We then propose a novel algorithm named CREST that efficiently solves the RC problem by labeling each region with the heat value of its containing points. In CREST, we propose innovative techniques to avoid processing expensive RNN queries and greatly reduce the number of region labeling operations. We perform detailed analyses on the complexity of CREST and lower bounds of the RC problem, and prove that CREST is asymptotically optimal in the worst case. Extensive experiments with both real and synthetic data sets demonstrate that CREST outperforms alternative algorithms by several orders of magnitude.Comment: Accepted to appear in ICDE 201

New Variations of the Maximum Coverage Facility Location Problem

Consider a competitive facility location scenario where, given a set U of n users and a set F of m facilities in the plane, the objective is to place a new facility in an appropriate place such that the number of users served by the new facility is maximized. Here users and facilities are considered as points in the plane, and each user takes service from its nearest facility, where the distance between a pair of points is measured in either L1 or L2 or L∞ metric. This problem is also known as the maximum coverage (MaxCov) problem. In this paper, we will consider the k-MaxCov problem, where the objective is to place k (⩾1) new facilities such that the total number of users served by these k new facilities is maximized. We begin by proposing an O(nlogn) time algorithm for the k-MaxCov problem, when the existing facilities are all located on a single straight line and the new facilities are also restricted to lie on the same line. We then study the 2-MaxCov problem in the plane, and propose an O(n2) time and space algorithm in the L1 and L∞ metrics. In the L2 metric, we solve the 2-MaxCov problem in the plane in O(n3logn) time and O(n2logn) space. Finally, we consider the 2-Farthest-MaxCov problem, where a user is served by its farthest facility, and propose an algorithm that runs in O(nlogn) time, in all the three metrics

Reverse Thinking in Spatial Queries

In recent years, an increasing number of researches are conducted on spatial queries regarding the influence of query objects. Among these queries, reverse k nearest neighbors (RkNN) query is the one studied the most extensively. Reverse k furthest neighbors (RkFN) queries is the natural complement of RkNN queries. RkNN query is introduced to reflect the influence of the query object. Since this representation is intuitive, RkNN query has attracted significant attention among the database community. Later, reverse top-k queries was introduced, and also used extensively to represent influence. In many scenarios, when we consider the influence of an spatial object, reverse thinking is involved. That is, whether an object is influential to another object is depending on how the other object assess this object, other than how this object considers the other object. In this thesis, we study three problems involves reverse thinking. We first study the problem of efficiently computing RkFN queries. We are the first to propose a solution for arbitrary value of k. Based on several interesting observations, we present an efficient algorithm to process the RkFN queries. We also present a rigorous theoretical analysis to study various important aspects of the problem and our algorithm. An extensive experimental study demonstrates that our algorithm outperforms the state-of-the-art algorithm even for k=1. The accuracy of our theoretical analysis is also verified. We then study the problem of selecting set of representative products considering both diversity and coverage based on reverse top-k queries. Since this problem is NP-hard, we employ a greedy algorithm. We adopt MinHash and KMV Synopses to assist set operations. Our experimental study demonstrates the performance of the proposed algorithm. We also study the problem of maximizing spatial influence of facility bundle based on RkNN queries. We are the first to study this problem. We prove its NP-hardness, and propose a branch-and-bound best first search algorithm that greedily select the currently best facility until we get the required number of facilities. We introduce the concept of kNN region. It allows us to avoid redundant calculation with dynamic programming technique. Experiments show that our algorithm is orders of magnitudes better than our baseline algorithm

Predicting optimal facility location without customer locations

Deriving meaningful insights from location data helps businesses make better decisions. One critical decision made by a business is choosing a location for its new facility. Optimal location queries ask for a location to build a new facility that optimizes an objective function. Most of the existing works on optimal location queries propose solutions to return best location when the set of existing facilities and the set of customers are given. However, most businesses do not know the locations of their customers. In this paper, we introduce a new problem setting for optimal location queries by removing the assumption that the customer locations are known. We propose an optimal location predictor which accepts partial information about customer locations and returns a location for the new facility. The predictor generates synthetic customer locations by using given partial information and it runs optimal location queries with generated location data. Experiments with real data show that the predictor can find the optimal location when sufficient information is provided. © 2017 Copyright held by the owner/author(s)

On Semantic Caching and Query Scheduling for Mobile Nearest-Neighbor Search

Location-based services have received increasing attention in recent years. In this paper, we address the performance issues of mobile nearest-neighbor search, in which the mobile user issues a query to retrieve stationary service objects nearest to him/her. An index based on Voronoi Diagram is used in the server to support such a search, while a semantic cache is proposed to enhance the access e ciency of the service. Cache replacement policies tailored for the proposed semantic cache are examined. Moreover, several query scheduling policies are proposed to address the inter-cell roaming issues in multi-cell environments. Simulations are conducted to evaluate the proposed methods. The result shows that the system performance, in terms of cache hit ratio, query response time, cell-cross number and cell-recross number, is improved signi cantly

New Applications of the Nearest-Neighbor Chain Algorithm

The nearest-neighbor chain algorithm was proposed in the eighties as a way to speed up certain hierarchical clustering algorithms. In the first part of the dissertation, we show that its application is not limited to clustering. We apply it to a variety of geometric and combinatorial problems. In each case, we show that the nearest-neighbor chain algorithm finds the same solution as a preexistent greedy algorithm, but often with an improved runtime. We obtain speedups over greedy algorithms for Euclidean TSP, Steiner TSP in planar graphs, straight skeletons, a geometric coverage problem, and three stable matching models. In the second part, we study the stable-matching Voronoi diagram, a type of plane partition which combines properties of stable matchings and Voronoi diagrams. We propose political redistricting as an application. We also show that it is impossible to compute this diagram in an algebraic model of computation, and give three algorithmic approaches to overcome this obstacle. One of them is based on the nearest-neighbor chain algorithm, linking the two parts together