Efficient algorithms for distance-based representative skyline computation in 2D space

Representative skyline computation is a fundamental issue in database area, which has attracted much attention in recent years. A notable definition of representative skyline is the distance-based representative skyline (DBRS). Given an integer k, a DBRS includes k representative skyline points that aims at minimizing the maximal distance between a non-representative skyline point and its nearest representative. In the 2D space, the state-of-the-art algorithm to compute the DBRS is based on dynamic programming (DP) which takes O(km²) time complexity, where m is the number of skyline points. Clearly, such a DP-based algorithm cannot be used for handling large scale dataset due to the quadratic time cost. To overcome this problem, in this paper, we propose a new approximate algorithm called ARS, and a new exact algorithm named PSRS, based on a carefully-designed parametric search technique. We show that the ARS algorithm can guarantee a solution that is at most ε larger than the optimal solution. The proposed ARS and PSRS algorithms run in O(k log² mlog(T/ε)) and O(k² log³ m) time respectively, where T is no more than the maximal distance between any two skyline points. We conduct extensive experimental studies over both synthetic and real-world datasets, and the results demonstrate the efficiency and effectiveness of the proposed algorithms.