Trajectory Clustering and \(k\)-NN for Robust Privacy Preserving \(k\)-NN Query Processing in GeoSpark  
[PERSON]  
1 Computer Engineering and Informatics Department, University of Patras, 265 04 Patras, Greece; [EMAIL_ADDRESS] (A.K. ); [EMAIL_ADDRESS] (M.T. ); [EMAIL_ADDRESS] (G.V. ); [EMAIL_ADDRESS] (S.S.); [EMAIL_ADDRESS] (A.T.)  
[PERSON]  
1 Computer Engineering and Informatics Department, University of Patras, 265 04 Patras, Greece; [EMAIL_ADDRESS] (A.K. ); [EMAIL_ADDRESS] (M.T. ); [EMAIL_ADDRESS] (G.V. ); [EMAIL_ADDRESS] (S.S.); [EMAIL_ADDRESS] (A.T.)  
[PERSON]  
2 Computer Engineering and Informatics Department, University of Patras, 265 04 Patras, Greece; [EMAIL_ADDRESS] (A.K. ); [EMAIL_ADDRESS] (M.T. ); [EMAIL_ADDRESS] (G.V. ); [EMAIL_ADDRESS] (S.S.); [EMAIL_ADDRESS] (A.T.)  
[PERSON]  
3 Computer Engineering and Informatics Department, University of Patras, 265 04 Patras, Greece; [EMAIL_ADDRESS] (A.K. ); [EMAIL_ADDRESS] (M.T. ); [EMAIL_ADDRESS] (G.V. ); [EMAIL_ADDRESS] (S.S.); [EMAIL_ADDRESS] (A.T.)  
[PERSON]  
1 Computer Engineering and Informatics Department, University of Patras, 265 04 Patras, Greece; [EMAIL_ADDRESS] (A.K. ); [EMAIL_ADDRESS] (M.T. ); [EMAIL_ADDRESS] (G.V. ); [EMAIL_ADDRESS] (S.S.); [EMAIL_ADDRESS] (A.T.)  
Footnote 1: email: {[[https://www.mdpi.com/journal/algorithms/article/pdf/1609989](https://www.mdpi.com/journal/algorithms/article/pdf/1609989)]([https://www.mdpi.com/journal/algorithms/article/pdf/1609989](https://www.mdpi.com/journal/algorithms/article/pdf/1609989))  
of databases, due to its computational complexity. Hence, the data mining techniques should be able to encounter data scalability, dimensionality, uncertain data and/or data preprocessing. Data preprocessing constitutes an important step before the data mining process and, as a result, data mining algorithms are designed to accept specific data formats that are best suited for them. With the advances in wireless and mobile technologies, moving objects are equipped with location positioning sensors and wireless communicating capabilities, thus, large-scale spatio-temporal data is being generated and an urgent need for efficient query processing approaches, to deal with both the spatial and temporal attributes, has been arisen [4]. In particular, with the advent of mobile and ubiquitous computing, spatio-temporal queries processing on moving objects databases has become a necessity for many applications, such as traffic control systems, geographical information systems, and location-aware advertisement. Hence, time-dependent versions of \(k\) nearest neighbor (\(k\)-NN) queries need to be studied. According to [5], the \(k\)-NN queries can be distinguished into four categories: (i) both query and data objects are static, (ii) moving query but static data objects, (iii) static query but moving data objects and (iv) both query and data objects are moving. When a mobile object's location data changes, a Snapshot \(k\)-NN (\(SkNN\)) query is issued at each location. However, in highly dynamic spatio-temporal applications, where the moving objects data varies frequently over time, a fundamental query is the so-called Continuous \(k\)-NN (\(CkNN\)) [6]. A \(CkNN\) query can be subjected to the fourth category, as it instantly retrieves the \(k\) nearest neighbor objects of a moving query object at each time within a given time interval. Practically, the \(CkNN\) spatio-temporal query is evaluated on a high number of consecutive timestamps and can be considered as a series of frequent \(SkNN\) queries. To the best of our knowledge, none of the existing approaches, such as [6; 7; 8] to name a few, address the problem of \(CkNN\) queries processing on non-linear trajectories under the support of Hough transformation. It is worth to mention that in previous works the process of \(CkNN\) query has been considered in road networks with linear trajectory moving objects. In this paper, our efforts are devoted to processing a \(CkNN\) query assuming that each object keeps track of non-linear trajectory.