Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things

Xiujun Wang, Zhi Liu, Yan Gao, Xiao Zheng, Xianfu Chen, Celimuge Wu

    Research output: Contribution to journalArticleScientificpeer-review

    10 Citations (Scopus)


    The approximate range emptiness problem requires a memory-efficient data structure D to approximately represent a set S of n distinct elements chosen from a large universe U= {0,1,⋯,N-1} and answer an emptiness query of the form “S∩[a;b]=0?” for an interval [a;b] of length L (a,b∈U), with a false positive rate ε. The designed D for this problem can be kept in high-speed memory and quickly determine approximately whether a query interval is empty or not. Thus, it is crucial for facilitating online query processing in the information-centric Internet of Things applications, where the IoT data are continuously generated from a large number of resource-constrained sensors or readers and then are processed in networks. However, the existing works on the approximate range emptiness problem only consider the simple case when the set S is static, rendering them unsuitable for the continuously generated IoT data. In this paper, we study the approximate range emptiness problem over sliding windows in the IoT Data streams, denoted by ε-ARESD-problem, where both insertion and deletion are allowed. We first prove that, given a sliding window size n and an interval length L, the lower bound of memory bits needed in any data structure for ε-ARESD-problem is n log 2 (nL/ε)+Θ(n). Then, a data structure is proposed and proved to be within a factor of 1.33 of the lower bound. The extensive simulation results demonstrate the advantage of the efficiency of our data structure over the baseline approach.
    Original languageEnglish
    Article number8633895
    Pages (from-to)21857-21869
    Number of pages13
    JournalIEEE Access
    Publication statusPublished - 4 Feb 2019
    MoE publication typeNot Eligible


    • Approximate range emptiness
    • data structure
    • information-centric network
    • Internet of Things
    • space lower bound


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