J. Parallel Distrib. Comput. 74 (2014) 3128–3140 Contents lists available at ScienceDirect J. Parallel Distrib. Comput. journal homepage: www.elsevier.com/locate/jpdc Peer-to-peer bichromatic reverse nearest neighbours in mobile ad-hoc networks Thao P. Nghiem a,∗ , Kiki Maulana a , Kinh Nguyen b , David Green a , Agustinus Borgy Waluyo a , David Taniar a a Faculty of Information Technology, Monash University, Melbourne, Australia b Faculty of Science, Technology and Engineering, La Trobe University, Melbourne, Australia highlights • Introducing a new direction in mobile P2P query processing for RNN queries. • Proposing and evaluating three different search algorithms: BFA, RBA and TBA. • Substantially saving more time and energy compared with the centralised system. • TBA outperforms by filtering unnecessary peers and maintaining high accuracy rate. article info Article history: Received 7 September 2013 Received in revised form 19 April 2014 Accepted 29 July 2014 Available online 12 August 2014 Keywords: Reverse nearest neighbours P2P spatial queries Mobile database Mobile ad-hoc networks Collaborative caching abstract The increasing use of mobile communications has raised many issues of decision support and resource allocation. A crucial problem is how to solve queries of Reverse Nearest Neighbour (RNN). An RNN query returns all objects that consider the query object as their nearest neighbour. Existing methods mostly rely on a centralised base station. However, mobile P2P systems offer many benefits, including self-organisation, fault-tolerance and load-balancing. In this study, we propose and evaluate 3 distinct P2P algorithms focusing on bichromatic RNN queries, in which mobile query peers and static objects of interest are of two different categories, based on a time-out mechanism and a boundary polygon around the mobile query peers. The Brute-Force Search Algorithm provides a naive approach to exploit shared information among peers whereas two other Boundary Search Algorithms filter a number of peers involved in query processing. The algorithms are evaluated in the MiXiM simulation framework with both real and synthetic datasets. The results show the practical feasibility of the P2P approach for solving bichromatic RNN queries for mobile networks. © 2014 Elsevier Inc. All rights reserved. 1. Introduction The growing importance of mobile communication systems has highlighted the need for solutions to many problems of geographic searching. One of these needs is the problem of Reverse Nearest Neighbour (RNN), in which a query returns all objects that consider the query object as their nearest neighbour. Reverse Nearest Neighbour (RNN) queries were first introduced in 2000 by Korn and Muthukrishnan [14]. They have since attracted a growing number of studies in a wide range of applications, such as decision support systems, mobile navigation systems and resource ∗ Corresponding author. E-mail address: phuong.thao.nghiem@monash.edu (T.P. Nghiem). allocation. The problem is raised from the objects’ point of view. Instead of finding the nearest objects from the query point q, it asks which objects consider q as their nearest neighbour. There are two types of RNNs. Firstly monochromatic RNN (MRNN), in which query objects and objects of interest are of the same category. A typical example of MRNN is that in mixed reality games such as BotFighter, players need to shoot only other players who are the closest to them. Therefore, the strategy is finding her own reverse nearest neighbours to avoid their shootings. Secondly, bichromatic RNN (BRNN), in which they are of different categories. Specifically, in MRNN, we have all objects are of the same type and the answer of a MRNN from a query object q ∈ 0 is MRNN (q) = {o i ∈ O|∀o j ∈ O, dis E (q, o i ) ≤ dis E (o j , o i )}, where dis E (, ) is the Euclidean distance function. The problem becomes more challenging in BRNN since there are two distinct types of objects: P and O in the network as illustrated in Fig. 1. The return of BRNN http://dx.doi.org/10.1016/j.jpdc.2014.07.007 0743-7315/© 2014 Elsevier Inc. All rights reserved.