HPC - privacy model for collaborative skyline processing

Abstract

In general, skyline query is defined as finding a set of interesting database objects, which are not dominated to one another objects. A typical example is to find the hotel that is cheap and close to the beach. Since the introduction of skyline operator by Borzsonyi et al into database community, there has been a number of research works evolving and related publications related in last decade. However, there is only a few of them working on distributed skyline processing in collaborative computing environments. None of them considered the issue of privacy enforcement. The problem is that server has to disclose the sub-skylines (the actual skyline points) without privacy protection. In this paper, we propose the Hierarchical Piecewise Curve (HPC) model to enforce privacy during collaborative skyline processing and the private information can be released in a hierarchically controllable manner. Firstly we develop the polynomial expressions of Piecewise Curve (PC) by Spline interpolation to approximate the actual sub-skyline points. Figure 1 graphically showed the approximation. With Spline function, PC in R knocks are defined as: equations where there is no intersection among all knocks and the corresponding Mean Square Error (MSE) is defined as: equations. Secondly, we define the operators for the PC. If we have two servers working on the skyline query, we may have two Curve, c1 and c2 with respective intervals as a ≤ x ≤ b and n ≤ x ≤ m. We observed that there are 3 categories of relationships. First, c1 totally dominates c2; Second, c1 and c2 are totally independent; Third, c1 partially dominates c2. In the experiments, we observe that increasing the order of the polynomial and/or the number of PC resulted in reduction of MSE. Moreover, we observed the performance dropped when number of object in database increased. Meanwhile, the performance of skyline processing by the HPC model with 10 servers and 20 servers were relatively static when the database size increased. The poor performance of traditional approach was bottlenecked at constructing the global database for computing the global skyline. In the contrary, HPC model enabled distributed sub-skyline processing. Although there was computation overhead for merging curves (by equation 13), it could take advantage of distributing skyline computation among servers. Technically, we demonstrated Piecewise Curves (PC) as an answer approximation to response to the skyline query instead of actual skyline points. From the preliminary experimental results, we observed that the performance of HPC model for skyline processing out performance the traditional approach in distributed and cooperative computing environments.