{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:38:12Z","timestamp":1761676692255,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61402094"],"award-info":[{"award-number":["61402094"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2016501076"],"award-info":[{"award-number":["F2016501076"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005047","name":"Natural Science Foundation of Liaoning Province","doi-asserted-by":"publisher","award":["201602254"],"award-info":[{"award-number":["201602254"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["N172304022"],"award-info":[{"award-number":["N172304022"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In recent years, energy-efficient data collection has evolved into the core problem in the resource-constrained Wireless Sensor Networks (WSNs). Different from existing data collection models in WSNs, we propose a collaborative data collection scheme based on optimal clustering to collect the sensed data in an energy-efficient and load-balanced manner. After dividing the data collection process into the intra-cluster data collection step and the inter-cluster data collection step, we model the optimal clustering problem as a separable convex optimization problem and solve it to obtain the analytical solutions of the optimal clustering size and the optimal data transmission radius. Then, we design a Cluster Heads (CHs)-linking algorithm based on the pseudo Hilbert curve to build a CH chain with the goal of collecting the compressed sensed data among CHs in an accumulative way. Furthermore, we also design a distributed cluster-constructing algorithm to construct the clusters around the virtual CHs in a distributed manner. The experimental results show that the proposed method not only reduces the total energy consumption and prolongs the network lifetime, but also effectively balances the distribution of energy consumption among CHs. By comparing it o the existing compression-based and non-compression-based data collection schemes, the average reductions of energy consumption are 17.9% and 67.9%, respectively. Furthermore, the average network lifetime extends no less than 20-times under the same comparison.<\/jats:p>","DOI":"10.3390\/s18082487","type":"journal-article","created":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T11:22:34Z","timestamp":1533122554000},"page":"2487","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Collaborative Data Collection Scheme Based on Optimal Clustering for Wireless Sensor Networks"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2360-7895","authenticated-orcid":false,"given":"Guorui","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haobo","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0865-3570","authenticated-orcid":false,"given":"Sancheng","family":"Peng","sequence":"additional","affiliation":[{"name":"Laboratory of Language Engineering and Computing, Guangdong University of Foreign Studies, Guangzhou 510006, China"},{"name":"School of Information Science and Technology, Guangdong University of Foreign Studies, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinguang","family":"Li","sequence":"additional","affiliation":[{"name":"Laboratory of Language Engineering and Computing, Guangdong University of Foreign Studies, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shui","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Software, University of Technology Sydney, Sydney 2007, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengfei","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"},{"name":"College of Information Science and Engineering, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11227-013-1021-9","article-title":"Wireless sensor networks: A survey on recent developments and potential synergies","volume":"68","author":"Rawat","year":"2014","journal-title":"J. Supercomput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1109\/COMST.2014.2320073","article-title":"Survey on the characterization and classification of wireless sensor network applications","volume":"16","author":"Borges","year":"2014","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.3390\/s16081318","article-title":"CS2-Collector: A new approach for data collection in wireless sensor networks based on two-dimensional compressive sensing","volume":"16","author":"Yong","year":"2016","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s11235-015-0092-8","article-title":"A comparative analysis of energy conservation approaches in hybrid wireless sensor networks data collection protocols","volume":"61","author":"Abdullah","year":"2016","journal-title":"Telecommun. Syst."},{"key":"ref_5","first-page":"1","article-title":"Compressive sensing in wireless sensor networks\u2014A survey","volume":"33","author":"Middya","year":"2016","journal-title":"IETE Tech. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Luo, J., Xiang, L., and Rosenberg, C. (2010, January 23\u201327). Does compressed sensing improve the throughput of wireless sensor networks?. Proceedings of the IEEE International Conference on Communications, Cape Town, South Africa.","DOI":"10.1109\/ICC.2010.5502565"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.adhoc.2016.04.008","article-title":"A survey on clustering techniques for cooperative wireless networks","volume":"47","author":"Sucasas","year":"2016","journal-title":"Ad Hoc Netw."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2017\/6457942","article-title":"Energy efficient hierarchical clustering approaches in wireless sensor networks: A survey","volume":"2017","author":"Jan","year":"2017","journal-title":"Wirel. Commun. Mobile Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s11277-017-5047-9","article-title":"A compressed sensing approach to resolve the energy hole problem in large scale WSNs","volume":"99","author":"Singh","year":"2018","journal-title":"Wirel. Pers. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1504\/IJSNET.2018.090141","article-title":"In-network data processing in wireless sensor networks using compressed sensing","volume":"26","author":"Singh","year":"2018","journal-title":"Int. J. Sens. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2550","DOI":"10.1109\/JSEN.2017.2669081","article-title":"A compressibility-based clustering algorithm for hierarchical compressive data gathering","volume":"17","author":"Lan","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"24391","DOI":"10.1109\/ACCESS.2018.2832626","article-title":"Compressive data gathering based on even clustering for wireless sensor networks","volume":"6","author":"Qiao","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4257","DOI":"10.1109\/TVT.2014.2361250","article-title":"Treelet-based clustered compressive data aggregation for wireless sensor networks","volume":"64","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7553","DOI":"10.1109\/ACCESS.2017.2696745","article-title":"Unbalanced expander based compressive data gathering in clustered wireless sensor networks","volume":"5","author":"Li","year":"2017","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3629","DOI":"10.1109\/TIT.2007.904835","article-title":"Joint source-channel communication for distributed estimation in sensor networks","volume":"53","author":"Bajwa","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Luo, C., Wu, F., Sun, J., and Chen, C.W. (2009, January 20\u201325). Compressive data gathering for large-scale wireless sensor networks. Proceedings of the International Conference on Mobile Computing and Networking, Beijing, China.","DOI":"10.1145\/1614320.1614337"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1722","DOI":"10.1109\/TNET.2012.2229716","article-title":"Compressed data aggregation: energy-efficient and high-fidelity data collection","volume":"21","author":"Xiang","year":"2013","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TPDS.2014.2308212","article-title":"Data gathering with compressive sensing in wireless sensor networks: A random walk based approach","volume":"26","author":"Zheng","year":"2015","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.inffus.2013.07.001","article-title":"Information extraction from sensor networks using the Watershed transform algorithm","volume":"22","author":"Hammoudeh","year":"2015","journal-title":"Inf. Fusion"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1109\/LCOMM.2016.2519031","article-title":"Neighbor-aided spatial-temporal compressive data gathering in wireless sensor networks","volume":"20","author":"Quan","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1109\/TWC.2012.121412.120148","article-title":"STCDG: An efficient data gathering algorithm based on matrix completion for wireless sensor networks","volume":"12","author":"Cheng","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"23137","DOI":"10.3390\/s141223137","article-title":"Correlated spatio-temporal data collection in wireless sensor networks based on low rank matrix approximation and optimized node sampling","volume":"14","author":"Piao","year":"2014","journal-title":"Sensors"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1109\/TMC.2016.2595569","article-title":"Recover corrupted data in sensor networks: A matrix completion solution","volume":"16","author":"Xie","year":"2017","journal-title":"IEEE Trans. Mobile Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Candes","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1109\/JCN.2013.000083","article-title":"Compressive sensing: From theory to applications, a survey","volume":"15","author":"Qaisar","year":"2013","journal-title":"J. Commun. Netw."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2016\/4156358","article-title":"Data gathering techniques for wireless sensor networks: A comparison","volume":"12","author":"Campobello","year":"2016","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","article-title":"Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information","volume":"52","author":"Candes","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","article-title":"Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems","volume":"1","author":"Figueiredo","year":"2008","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3301","DOI":"10.1109\/TSP.2015.2421476","article-title":"Homotopy based algorithms for l0-regularized least-squares","volume":"63","author":"Soussen","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3029","DOI":"10.1109\/TIT.2017.2686880","article-title":"Partial hard thresholding","volume":"63","author":"Jain","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2419","DOI":"10.1007\/s11235-011-9564-7","article-title":"Localization algorithms of wireless sensor networks: A survey","volume":"52","author":"Han","year":"2013","journal-title":"Telecommun. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1002\/tee.21747","article-title":"An unequal clustering algorithm based on energy balance for wireless sensor networks","volume":"7","author":"Xu","year":"2012","journal-title":"IEEJ Trans. Electr. Electron. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.comcom.2012.10.006","article-title":"COCA: Constructing optimal clustering architecture to maximize sensor network lifetime","volume":"36","author":"Li","year":"2013","journal-title":"Comput. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"13117","DOI":"10.1109\/ACCESS.2018.2797885","article-title":"A grid-based clustering algorithm via load analysis for industrial Internet of things","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1049\/iet-ipr.2010.0242","article-title":"Approximately even partition algorithm for coding the Hilbert curve of arbitrary-sized image","volume":"6","author":"Wu","year":"2012","journal-title":"IET Image Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1109\/TPDS.2013.90","article-title":"Transmission-efficient clustering method for wireless sensor networks using compressive sensing","volume":"25","author":"Xie","year":"2014","journal-title":"IEEE Trans. Parallel Distrib. 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