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

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 interva...

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Main Authors: Xiujun Wang, Zhi Liu, Yan Gao, Xiao Zheng, Xianfu Chen, Celimuge Wu
Format: Article
Language:English
Published: IEEE 2019-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/8633895/
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spelling doaj-4ebf4187974344d3b524eb07714659cb2021-03-29T22:00:31ZengIEEEIEEE Access2169-35362019-01-017218572186910.1109/ACCESS.2019.28971548633895Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of ThingsXiujun Wang0https://orcid.org/0000-0002-8758-5763Zhi Liu1Yan Gao2Xiao Zheng3Xianfu Chen4Celimuge Wu5School of Computer Science and Technology, Anhui University of Technology, Ma&#x2019;anshan, ChinaDepartment of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu, JapanSchool of Computer Science and Technology, Anhui University of Technology, Ma&#x2019;anshan, ChinaSchool of Computer Science and Technology, Anhui University of Technology, Ma&#x2019;anshan, ChinaVTT Technical Research Centre of Finland Ltd., Oulu, FinlandDepartment of Computer and Network Engineering, Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, JapanThe 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,&#x22EF;,N-1} and answer an emptiness query of the form &#x201C;S&#x2229;[a;b]=0?&#x201D; for an interval [a;b] of length L (a,b&#x2208;U), with a false positive rate &#x03B5;. 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 &#x03B5;-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 &#x03B5;-ARESD-problem is n log<sub>2</sub> (nL/&#x03B5;)+&#x0398;(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.https://ieeexplore.ieee.org/document/8633895/Approximate range emptinessdata structureinformation-centric networkInternet of Thingsspace lower bound
collection DOAJ
language English
format Article
sources DOAJ
author Xiujun Wang
Zhi Liu
Yan Gao
Xiao Zheng
Xianfu Chen
Celimuge Wu
spellingShingle Xiujun Wang
Zhi Liu
Yan Gao
Xiao Zheng
Xianfu Chen
Celimuge Wu
Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things
IEEE Access
Approximate range emptiness
data structure
information-centric network
Internet of Things
space lower bound
author_facet Xiujun Wang
Zhi Liu
Yan Gao
Xiao Zheng
Xianfu Chen
Celimuge Wu
author_sort Xiujun Wang
title Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things
title_short Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things
title_full Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things
title_fullStr Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things
title_full_unstemmed Near-Optimal Data Structure for Approximate Range Emptiness Problem in Information-Centric Internet of Things
title_sort near-optimal data structure for approximate range emptiness problem in information-centric internet of things
publisher IEEE
series IEEE Access
issn 2169-3536
publishDate 2019-01-01
description 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,&#x22EF;,N-1} and answer an emptiness query of the form &#x201C;S&#x2229;[a;b]=0?&#x201D; for an interval [a;b] of length L (a,b&#x2208;U), with a false positive rate &#x03B5;. 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 &#x03B5;-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 &#x03B5;-ARESD-problem is n log<sub>2</sub> (nL/&#x03B5;)+&#x0398;(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.
topic Approximate range emptiness
data structure
information-centric network
Internet of Things
space lower bound
url https://ieeexplore.ieee.org/document/8633895/
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