A Pruning Algorithm for Reverse Nearest Neighbors in Directed Road Networks

International Journal of Networked and Distributed Computing, Vol. 3, No. 4 (November 2015), 261-272 A Pruning Algorithm for Reverse Nearest Neighbors in Directed Road Networks Rizwan Qamar 1 , Muhammad Attique 2 , Tae-Sun Chung 3 1 Computer Engineering, Ajou University, Paldal Hall 913-2, Suwon, Gyeonggi-do 443-749, South Korea E-mail: 2 Computer Engineering, Ajou University, Paldal Hall 913-2, Suwon, Gyeonggi-do 443-749, South Korea E-mail: 3 Computer Engineering, Ajou University, Paldal Hall 913-2, Suwon, Gyeonggi-do 443-749, South Korea E-mail: Abstract In this paper, we studied the problem of continuous reverse k nearest neighbors (RkNN) in directed road network, where a road segment can have a particular orientation. A RNN query returns a set of data objects that take query point as their nearest neighbor. Although, much research has been done for RNN in Euclidean and undirected network space, very less attention has been paid to directed road network, where network distances are not symmetric. In this paper, we provided pruning rules which are used to minimize the network expansion while searching for the result of a RNN query. Based on these pruning rules we provide an algorithm named SWIFT for answering RNN queries in continuous directed road network. Keywords: reverse nearest neighbors, spatial query, directed road network, continuous. 1. Introduction Spatial databases offer large number of services such as nearest neighbor, resource allocation, and preferential search etc. These services have not only changed peoples daily life but also scientific research. For example, people now rely on locationbased services to plan and manage their trips. This new demand for location-aware services has resulted in development of efficient algorithms and many novel query types for spatial databases. One of them is reverse nearest neighbor (RkNN). While a lot of attention has been given to this problem because of its practical applicability [1–3], most of it exclusively focuses on Euclidian space or undirected road network. In this paper, we study safe region of a reverse nearest neighbor query for a moving query and static data objects in a directed road network(i.e., Published by Atlantis Press Copyright: the authors 261 R. Qamar et al. each road is either directed or undirected). A safe region is a region in which result of the query doesn’t change when the query object moves within safe region. p3 p1 q crease the frequency of updates. However, just increasing the frequency of queries doesn’t not guarantee freshness of result and the it may become invalid in between two timestamps. Moreover this not only increases the load on server but also increases the use of communication channel between client and the server. The contributions of this paper are as following: • We present an algorithm for calculation of moving p2 RkNN in a directed road networks. • We provide a pruning rule that minimizes the net- Fig. 1. Example Road Network Consider a query point q and a set O of points of interest (POIs) e.g. offices, universities, schools etc. We use d(q, o) to denote network distance from query object q to data object o. Given a query point q, RkNN query returns a set of data points o ∈ O such that q is one of there k nearest neighbor i.e. RkNN(q) = o ∈ d(o, q)  d(o, ok ) where ok is the kth nearest neighbor of data point o. Many reallife scenarios exist to illustrate the importance of continuous reverse nearest neighbor queries. Consider a first person shooting game in which the goal of each player is to shoot the other player. Naturally, all players try to avoid getting shot and for this they continuously monitor their own reverse nearest neighbor as chances of getting shot from the reverse nearest neighbor are highest. Fig. 1 illustrates such game, where p1 is closest to q but RNN of q is p2 as nearest neighbor of p1 is p3 . RkNN has received a lot of attention [4–6] from the research community for applications like emergency response team and taxi providing services. In general, RkNN query can further be classified into two groups monochromatic and biochromatic. Our example above is of monochromatic RkNN query where all objects belong to the same set of objects. Consider the example of taxi and customers where they belong to the set of taxis and customers respectively. In general, the main problem in continuous reverse nearest neighbor query is how to maintain the freshness of the query result, as the query object is moving freely and arbitrarily. A naı̈ve technique for finding RkNN of a moving query object q is to in- work expansion for finding RkNN in directed road networks. • We discuss why RkNN algorithm for undirected road is not applicable to directed road networks. • We conduct experiments to study the effects of various parameters and show superiority of SWIFT over naı̈ve algorithm. The remainder of this paper is structured as follows. Section 2 surveys related work and limitation of undirected algorithms. Section 3 explains terms and definitions used in this paper as well as gives explanation about the problem and some pruning rules. Section 4 explains the working of SWIFT algorithm. Section 5 discusses SWIFT in continuous road network. Section 6 discusses the experimental results. Section 7 gives concluding remarks and future way through. 2. Related Work Section 2.1 surveys RkNN in spatial databases and Section 2.2 discusses why undirected algorithms are not applicable to directed road networks. 2.1. Reverse Nearest Neighbor in Euclidean and Road Networks RkNN was first introduced by Korn et al. [1] where they used pre-computations to answer the RNN for a query object q. Drawback of this technique was that they were only able to answer RkNN query for a fixed value of k. Stanoi et al. [7] proposed an algorithm that did not require preprocessing. They proposed partitioning algorithm that divides the whole Published by Atlantis Press Copyright: the authors 262 Instructions for Typesetting Manuscripts Using LATEX n4 o2 2 2 n4 1 q 1 o1 o2 2 2 1 n2 n3 1 2 2 1 n1 n3 1 1 q n1 (a) 1 o1 n2 (b) Figure 2: Examples (a) undirected road network (b) directed road network space into six equal regions of 60◦ . It can be verified that the possible RNN of q can only be the nearest point to q found in each of the six regions. This proves that in 2D space, there can be at most six RNNs for a query point q. Sun et al. [3] presented a continuous monitoring in bichromatic RkNN queries. They used multiway tree with each query to assign it a monitoring region and only updates in the monitoring region affects the result. However, it is only applicable to bichromatic queries and can only answer queries when k = 1. Cheema et al. [5] presented continuous reverse nearest neighbor queries for both Euclidian and spatial road network and suggested pruning rules for road networks. Similarly, Man L Yiu. [4] proposed a method for finding RkNN in an undirected (...truncated)