Abstract
Given two object sets P and Q, a k-closest pairs (k-CP) query finds k closest object pairs from P×Q. This operation is common in many real-life applications such as GIS, data mining and recommender systems. However, the k-CP problem has not been well studied in Dynamic Cyber-Physical-Social Systems (D-CPSS), where temporal information and multiple attributes are associated with each edge. In D-CPSS, people would like to specify multiple constraints on these attributes within a time interval to illustrate their requirements. In this paper, we study the temporal multiple constraints k closest pairs (TMC-k-CP) in D-CPSS, which is NP-Complete. We propose a divide-and-conquer cloud-based algorithm (DC) to find TMC-k-CP efficiently and effectively. To the best of our knowledge, DC is the first algorithm supporting the TMC-k-CP query in D-CPSS. The experimental results on eight real D-CPSS datasets demonstrate that our algorithm outperforms the state-of-the-art methods in terms of both efficiency and effectiveness.
Highlights
INTRODUCTION kClosest Pairs Query (k-CPQ) has attracted the attention of billions of people and been widely used in many applications, such as urban planning [19], [29], resource management and recommender systems [2], [6], [26]–[28]
Given two spatial object sets P and Q, a kClosest Pairs Query (k-CPQ) returns k closest object pairs from P×Q according to a certain similarity metric, such as the minimum distance between two points of interest on a road network
More time will be needed to calculate the Temporal Shortest Path with MultiConstraints (TSP-MC) by Two-Pass and find the k closest pairs with multiple constraints; For BL, the reason is similar to divide-and-conquer cloud-based algorithm (DC); (4) With the increase of the time interval, more temporal edges are included in the search
Summary
The main work of our study is to find the temporal multi-constraint k closest pairs, we define the TMC-k-CPQ problem in an ATG as follows. Input: An ATG GA, W constraints on attributes ΛW ), point sets P and Q, and a time interval [tα, tβ ]. Output: a set R = { p, q } of k pairs, where p, q ∈ P×Q, and p, q ∈ R have the kth shortest distance, and the temporal path from p to q satisfies the W constraints within the time interval [tα, tβ ]. TEMPORAL OBJECTIVE FUNCTION we propose a temporal objective function to investigate whether the aggregated attribute value of a temporal path satisfies the corresponding constraints. The temporal objective function of path pMvs,vd (t) is defined as below Eq(1): δ(pMvs,vd (t)) = max{. If the temporal path is feasible, δ(pMvs,vd (t)) ≤ 1, otherwise, δ(pMvs,vd (t)) > 1
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