Finding Pareto optimal groups

Abstract

Skyline computation, aiming at identifying a set of skyline points that are not dominated by any other point, is particularly useful for multi-criteria data analysis and decision making. Traditional skyline computation, however, is inadequate to answer queries that need to analyze not only individual points but also groups of points. To address this gap, we generalize the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. In order to compute G-Skyline groups consisting of k points efficiently, we present a novel structure that represents the points in a directed skyline graph and captures the dominance relationships among the points based on the first k skyline layers. We propose efficient algorithms to compute the first k skyline layers. We then present two heuristic algorithms to efficiently compute the G-Skyline groups: the point-wise algorithm and the unit group-wise algorithm, using various pruning strategies. The experimental results on the real NBA dataset and the synthetic datasets show that G-Skyline is interesting and useful, and our algorithms are efficient and scalable.

Finding Group-Based Skyline over a Data Stream in the Sensor Network

“…In order to solve such problem in a better way, the group-based skyline query was proposed. The group-based skyline (G-Skyline for short) query is to identify the best groups not g-dominated by any other groups with the same group size, and paper [1] proposed two algorithms for computing G-Skyline. Different from the traditional skyline, the G-Skyline presents much more useful information in more complexity phenomena such as sensor network, multi-decision and data mining.…”

“…Different from the traditional skyline, the G-Skyline presents much more useful information in more complexity phenomena such as sensor network, multi-decision and data mining. In the above example, the G-Skyline groups with 2 points include {p 1 , p 6 }, {p 1 , p 11 }, {p 6 , p 11 }, {p 6 , p 3 }, {p 11 , p 8 }, {p 11 , p 10 }, then the fire force could consider selecting one group from the result.…”

“…Based on the data in Figure 1, we give an example of data stream in Figure 2. At first, there are 3 points {p 1 , p 2 , p 3 }, at moment t, a new point p 4 arrives, the active points are {p 1 , p 2 , p 3 , p 4 }, and at moment 2t, an old point p 2 expires, now the active points are {p 1 , p 3 , p 4 }. With the dataset changing, the groups set will also change, for example, at first, the groups with 2 points are {p 1 p 2 , p 2 p 3 , p 1 p 3 }, when the point p 4 arrives, the groups with 2 points change to {p 1 p 2 , p 1 p 3 , p 1 p 4 , p 2 p 3 , p 2 p 4 , p 3 p 4 }, the groups containing p 4 appear, when the point p 2 expires, the groups with 2 points change to {p 1 p 3 , p 1 p 4 , p 3 p 4 }, the groups containing p 2 are removed.…”

“…The naive method to find the G-Skyline over a data stream is to use the existing algorithm PWise in paper [1] directly when the data set changes. However, the data may change quickly in the data stream, under this circumstance, repeating PWise computation for the whole data set will need much time cost and much redundant computation.…”

“…The skyline of a data set includes all the points which are not worse than any other points. Given a data set D with d-dimension, every point q can be written as (q [1], q [2], . .…”