An Efficient Algorithm for Arbitrary Reverse Furthest Neighbor Queries

Liu, Jianquan; Chen, Hanxiong; Furuse, Kazutaka; Kitagawa, Hiroyuki

doi:10.1007/978-3-642-29253-8_6

Cited by 8 publications

(11 citation statements)

References 18 publications

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“…Multiple studies have focused on the efficient processing of sophisticated spatial queries based on the farthest neighbor search [6], [10], [12], [24]- [26], [42], [45], [47], [49], [50]. Curtin et al [10] reported an approximate farthest neighbor search algorithm that selects a set of candidate data points using data distributed in a Euclidean space.…”

Section: A Farthest Neighbor Search Algorithmsmentioning

confidence: 99%

“…For a set of data points P and a set of query points Q, an AkFN query returns k data points in P that have the largest aggregate distances to all query points in Q. Moreover, reverse farthest neighbor queries have been studied, in the Euclidean space [24], [50] and spatial networks [45], [49]. Yao et al [50] proposed progressive farthest cell and convex hull farthest cell algorithms to support the reverse farthest neighbor queries using an Rtree [4], [16].…”

Section: A Farthest Neighbor Search Algorithmsmentioning

confidence: 99%

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Group Processing of Multiple k-Farthest Neighbor Queries in Road Networks

Cho

Attique

2020

IEEE Access

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Advances in mobile technologies and map-based applications enables users to utilize sophisticated spatial queries, including k-nearest neighbor and shortest path queries. Often, location-based servers are used to handle multiple simultaneous queries because of the popularity of map-based applications. This study focuses on the efficient processing of multiple concurrent k-farthest neighbor (kFN) queries in road networks. For a positive integer k, query point q, and set of data points P , a kFN query returns k data points farthest from the query point q. For addressing multiple concurrent spatial queries, traditional locationbased servers based on one-query-at-a-time processing are unsuitable owing to high redundant computation costs. Therefore, we propose a group processing of multiple kFN (GMP) algorithm to process multiple kFN queries in road networks. The proposed GMP algorithm uses group computation to avoid the redundant computation of network distances between the query and data points. The experiments using real-world roadmaps demonstrate the proposed solution's effectiveness and efficiency. INDEX TERMS Spatial databases, group processing, multiple k-farthest neighbor query, road network.

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Section: A Farthest Neighbor Search Algorithmsmentioning

confidence: 99%

Section: A Farthest Neighbor Search Algorithmsmentioning

confidence: 99%

Group Processing of Multiple k-Farthest Neighbor Queries in Road Networks

Cho

Attique

2020

IEEE Access

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“…The k-Farthest MaxCov problem is the bi-chromatic version of reverse farthest neighbor problem for a set of k query points. The bi-chromatic reverse farthest neighbor problem and its application to spatial databases has been recently studied by Yao et al [33] and Liu et al [24].…”

Section: Potential Applicationsmentioning

confidence: 99%

New variations of the maximum coverage facility location problem

Bhattacharya

Nandy

2013

European Journal of Operational Research

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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 L 1 or L 2 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(n 2) time and space algorithm in the L 1 and L ∞ metrics. In the L 2 metric, we solve the 2-MaxCov problem in the plane in O(n 3 logn) time and O(n 2 logn) 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.

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“…In 2011, Gao et al [6] studied the aggregation k distant neighbor problem defined by the aggregation functions SUM, MAX and MIN, and presented the MB and BF algorithms based on R tree. In 2012, Liu et al [7] proposed the reverse farthest neighbor query algorithm without location restrictions, and compared it with the PIV algorithm proposed in 2010. In 2013, Said et al [8] proposed a collaborative filtering scheduling algorithm based on k distant neighborhood.…”

Section: Related Work a The Rearch Of Nearest And Farthest Neighmentioning

confidence: 99%

“…(6)Point p i , p j must be in the current round of minimal covering on the border, at this time it will be the first point with the first j point of attachment point set as the new circle's center. The distance between two points set for the new round radius, and then through the above steps will j−1 point before to join in this circle, each join point need to perform the next step (7). 7If point p k is on the outside of the current circle, that is, point p j must be on the boundary of the minimum covering circle of the first k points because of three points can determine a circle and the center of the common circle of these three points can be directly calculated.…”

Section: The V-ogrkfn Algorithmmentioning

confidence: 99%

A Voronoi-Based Group Reverse k Farthest Neighbor Query Method in the Obstacle Space

et al. 2020

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With the rapid development of intelligent transportation and geographic information system, spatial data query technology has attracted the attention of many scholars. Among them, the reverse farthest neighbor query from the data point to find the target point as its farthest adjacent data points, used to obtain target set of weak influence. Its research results have been widely applied to facility location, earthquake relief, marketing and other major areas. Thus, the research of reverse furthest neighbor query technology is of great significance. However, the existing methods only deal with a single query point, and do not consider how to obtain the optimal farthest neighbor position of group reverse when the number of query points changes from one to a group. In addition, considering it is difficult to avoid some geographical location restrictions in the real situation, the existing studies are limited to road network or Euclidean space simplely, without taking the existence of obstacles into consideration. To this end, this paper proposed the V-OGRkFN(Voronoi-Obstacle Group Reverse k Farthest Neighbor) algorithm. Firstly, the algorithm gets the minimum cover circle of query points which are considered into a whole. Secondly, we use the framework based on the filtering and refining process of query by pruning strategy based on Voronoi diagram's properties. Then we get the candidate set using the theorem of transformation between k nearest neighbors and k farthest neighbors. Finally, the refining algorithm is given to get the final results. V-OGRkFN algorithm shows great performance of reverse k farthest neighbor query through the specific comparative experimental analysis. INDEX TERMS Obstacle space, reverse farthest neighbor query, Voronoi diagram, minimum coverage circle.

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An Efficient Algorithm for Arbitrary Reverse Furthest Neighbor Queries

Cited by 8 publications

References 18 publications

Group Processing of Multiple k-Farthest Neighbor Queries in Road Networks

Group Processing of Multiple k-Farthest Neighbor Queries in Road Networks

New variations of the maximum coverage facility location problem

A Voronoi-Based Group Reverse k Farthest Neighbor Query Method in the Obstacle Space

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