{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:43:21Z","timestamp":1760143401939,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:00:00Z","timestamp":1706227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"\u201cConsejo Nacional de Humanidades Ciencias y Tecnolog\u00edas\u201d (CONAHCyT) of M\u00e9xico","award":["SIP 20240950"],"award-info":[{"award-number":["SIP 20240950"]}]},{"name":"\u201cInstituto Polit\u00e9cnico Nacional\u201d","award":["SIP 20240950"],"award-info":[{"award-number":["SIP 20240950"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>This paper presents the spectral gap-based topology control algorithm (SGTC) for wireless backhaul networks, a novel approach that employs the Laplacian Spectral Gap (LSG) to find expander-like graphs that optimize the topology of the network in terms of robustness, diameter, energy cost, and network entropy. The latter measures the network\u2019s ability to promote seamless traffic offloading from the Macro Base Stations to smaller cells by providing a high diversity of shortest paths connecting all the stations. Given the practical constraints imposed by cellular technologies, the proposed algorithm uses simulated annealing to search for feasible network topologies with a large LSG. Then, it computes the Pareto front of the set of feasible solutions found during the annealing process when considering robustness, diameter, and entropy as objective functions. The algorithm\u2019s result is the Pareto efficient solution that minimizes energy cost. A set of experimental results shows that by optimizing the LSG, the proposed algorithm simultaneously optimizes the set of desirable topological properties mentioned above. The results also revealed that generating networks with good spectral expansion is possible even under the restrictions imposed by current wireless technologies. This is a desirable feature because these networks have strong connectivity properties even if they do not have a large number of links.<\/jats:p>","DOI":"10.3390\/fi16020043","type":"journal-article","created":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T08:56:01Z","timestamp":1706259361000},"page":"43","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Spectral Gap-Based Topology Control Algorithm for Wireless Backhaul Networks"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3270-1675","authenticated-orcid":false,"given":"Sergio Jes\u00fas","family":"Gonz\u00e1lez-Ambriz","sequence":"first","affiliation":[{"name":"Centro de Investigaci\u00f3n y Desarrollo de Tecnolog\u00eda Digital, Instituto Polit\u00e9cnico Nacional, Tijuana 22435, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6733-9445","authenticated-orcid":false,"given":"Rolando","family":"Menchaca-M\u00e9ndez","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Ciudad de M\u00e9xico 07700, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5783-352X","authenticated-orcid":false,"given":"Sergio Alejandro","family":"Pinacho-Castellanos","sequence":"additional","affiliation":[{"name":"Corteza.ai, San Andr\u00e9s Cholula 72830, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1020-6806","authenticated-orcid":false,"given":"Mario Eduardo","family":"Rivero-\u00c1ngeles\u00a0","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Ciudad de M\u00e9xico 07700, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MCOM.2014.6815890","article-title":"Scenarios for 5G Mobile and Wireless Communications: The Vision of the Metis Project","volume":"52","author":"Osseiran","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1109\/TCCN.2020.3041851","article-title":"5G New Radio Unlicensed: Challenges and Evaluation","volume":"7","author":"Hirzallah","year":"2021","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2796","DOI":"10.1109\/TMC.2018.2886897","article-title":"Cost Efficiency Optimization of 5G Wireless Backhaul Networks","volume":"18","author":"Ge","year":"2019","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"102353","DOI":"10.1016\/j.adhoc.2020.102353","article-title":"An Overview of Massive MIMO Localization Techniques in Wireless Cellular Networks: Recent Advances and Outlook","volume":"111","author":"Alamu","year":"2021","journal-title":"Ad Hoc Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MNET.2014.6963798","article-title":"5G Wireless Backhaul Networks: Challenges and Research Advances","volume":"28","author":"Ge","year":"2014","journal-title":"IEEE Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.nancom.2018.12.002","article-title":"Antenna Subarray Management for Hybrid Beamforming in Millimeter-Wave Mesh Backhaul Networks","volume":"19","author":"Zhai","year":"2019","journal-title":"Nano Commun. Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1007\/s11277-021-08550-9","article-title":"Massive MIMO Systems for 5G Communications","volume":"120","author":"Khwandah","year":"2021","journal-title":"Wirel. Pers. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ali, M.Y., Hossain, T., and Mowla, M.M. (2019, January 26\u201328). A Trade-off between Energy and Spectral Efficiency in Massive MIMO 5G System. Proceedings of the 2019 3rd International Conference on Electrical, Computer & Telecommunication Engineering (ICECTE), Rajshahi, Bangladesh.","DOI":"10.1109\/ICECTE48615.2019.9303551"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s11277-021-08231-7","article-title":"Energy Efficiency Optimization for Massive MIMO Backhaul Networks with Imperfect CSI and Full Duplex Small Cells","volume":"119","author":"Rajoria","year":"2021","journal-title":"Wirel. Pers. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.phycom.2017.11.004","article-title":"A Comprehensive Survey: Small Cell Meets Massive Mimo","volume":"26","author":"Rajoria","year":"2018","journal-title":"Phys. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"155014771881728","DOI":"10.1177\/1550147718817289","article-title":"Demand-Aware Traffic Cooperation for Self-Organizing Cognitive Small-Cell Networks","volume":"15","author":"Yao","year":"2019","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chataut, R., and Akl, R. (2020). Massive MIMO Systems for 5G and beyond Networks\u2014Overview, Recent Trends, Challenges, and Future Research Direction. Sensors, 20.","DOI":"10.3390\/s20102753"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10270-017-0587-8","article-title":"A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph Transformation","volume":"18","author":"Kluge","year":"2017","journal-title":"Softw. Syst. Model."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1145\/1089733.1089736","article-title":"Topology Control in Wireless Ad Hoc and Sensor Networks","volume":"37","author":"Santi","year":"2005","journal-title":"ACM Comput. Surv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1007\/s11277-020-07331-0","article-title":"Topology Control Algorithms for Wireless Sensor Networks: A Review","volume":"113","author":"Singla","year":"2020","journal-title":"Wirel. Pers. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10107","DOI":"10.1016\/j.apm.2013.05.053","article-title":"Topology Control in the Mobile Ad Hoc Networks in Order to Intensify Energy Conservation","volume":"37","author":"Shirali","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_17","first-page":"9696348","article-title":"Context-Based Topology Control for Wireless Mesh Networks","volume":"2016","author":"Mudali","year":"2016","journal-title":"Mob. Inf. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.comcom.2015.01.005","article-title":"Joint Network Lifetime and Delay Optimization for Topology Control in Heterogeneous Wireless Multi-Hop Networks","volume":"59","author":"Gui","year":"2015","journal-title":"Comput. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.comcom.2020.10.010","article-title":"Joint Link-Level and Network-Level Reconfiguration for Urban Mmwave Wireless Backhaul Networks","volume":"164","author":"Liu","year":"2020","journal-title":"Comput. Commun."},{"key":"ref_20","unstructured":"Hoory, S., Linial, N., and Wigderson, A. (2023, December 29). Expander Graphs and Their Applications. Available online: https:\/\/www.ams.org\/journal-getitem?pii=S0273-0979-06-01126-8."},{"key":"ref_21","unstructured":"Kleinberg, J., and Rubinfeld, R. (1996, January 14\u201316). Short Paths in Expander Graphs. Proceedings of the 37th Conference on Foundations of Computer Science, Burlington, VT, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Spielman, D.A. (2007, January 21\u201323). Spectral Graph Theory and its Applications. Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS\u201907), Providence, RI, USA.","DOI":"10.1109\/FOCS.2007.56"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7093","DOI":"10.1109\/JSEN.2020.3043748","article-title":"Dynamic Spatial-Correlation-Aware Topology Control of Wireless Sensor Networks Using Game Theory","volume":"21","author":"Hu","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.jpdc.2017.10.005","article-title":"Topology Control for Minimizing Interference with Delay Constraints in an Ad Hoc Network","volume":"113","author":"Wu","year":"2018","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5742","DOI":"10.1109\/ACCESS.2016.2581187","article-title":"Multi-Objective Topology Planning for Microwave-Based Wireless Backhaul Networks","volume":"4","author":"Li","year":"2016","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Almohamad, A., Hasna, M.O., Khattab, T., and Haouari, M. (2019, January 22\u201325). An Efficient Algorithm for Dense Network Flow Maximization with Multihop Backhauling and Nfps. Proceedings of the 2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall), Honolulu, HI, USA.","DOI":"10.1109\/VTCFall.2019.8891190"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/MWC.2015.7306533","article-title":"MmWave Massive-MIMO-Based Wireless Backhaul for the 5G Ultra-Dense Network","volume":"22","author":"Gao","year":"2015","journal-title":"IEEE Wirel. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Talak, R., Karaman, S., and Modiano, E. (2017, January 10\u201314). Capacity and Delay Scaling for Broadcast Transmission in Highly Mobile Wireless Networks. Proceedings of the 18th ACM International Symposium on Mobile Ad Hoc Networking and Computing, Chennai, India.","DOI":"10.1145\/3084041.3084045"},{"key":"ref_29","first-page":"1409","article-title":"Small-World Regular Networks for Communication","volume":"67","author":"Pandey","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Attali, S., Parter, M., Peleg, D., and Solomon, S. (2018, January 16\u201318). Wireless Expanders. Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, Vienna, Austria.","DOI":"10.1145\/3210377.3210396"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Pandurangan, G., Robinson, P., and Trehan, A. (2014, January 19\u201323). Dex: Self-Healing Expanders. Proceedings of the 2014 IEEE 28th International Parallel and Distributed Processing Symposium, Phoenix, AZ, USA.","DOI":"10.1109\/IPDPS.2014.78"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Augustine, J., Pandurangan, G., Robinson, P., Roche, S., and Upfal, E. (2015, January 17\u201320). Enabling Robust and Efficient Distributed Computation in Dynamic Peer-to-Peer Networks. Proceedings of the 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, Berkeley, CA, USA.","DOI":"10.1109\/FOCS.2015.29"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1145\/3310165.3310170","article-title":"Toward Demand-Aware Networking","volume":"48","author":"Avin","year":"2019","journal-title":"ACM SIGCOMM Comput. Commun. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Khaturia, M., Appaiah, K., and Karandikar, A. (2019, January 15\u201318). On Efficient Wireless Backhaul Planning for the \u201cFrugal 5G\u201d Network. Proceedings of the 2019 IEEE Wireless Communications and Networking Conference Workshop (WCNCW), Marrakech, Morocco.","DOI":"10.1109\/WCNCW.2019.8902828"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Xu, X., Saad, W., Zhang, X., Xiao, L., and Zhou, S. (2016, January 16\u201318). Dynamic on\/off Control of Wireless Small Cells with Heterogeneous Backhauls. Proceedings of the 2016 23rd International Conference on Telecommunications (ICT), Thessaloniki, Greece.","DOI":"10.1109\/ICT.2016.7500346"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103269","DOI":"10.1016\/j.jnca.2021.103269","article-title":"Efficient Solutions to the Placement and Chaining Problem of User Plane Functions in 5G Networks","volume":"197","year":"2022","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"30386","DOI":"10.1109\/ACCESS.2021.3058619","article-title":"Evolutionary Algorithms for 5G Multi-Tier Radio Access Network Planning","volume":"9","author":"Ganame","year":"2021","journal-title":"IEEE Access"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.adhoc.2015.01.019","article-title":"Simulated Annealing for Interface-Constrained Channel Assignment in Wireless Mesh Networks","volume":"29","author":"Chen","year":"2015","journal-title":"Ad Hoc Netw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1734213.1734219","article-title":"Routing Betweenness Centrality","volume":"57","author":"Dolev","year":"2010","journal-title":"J. ACM"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2338","DOI":"10.1109\/TAC.2013.2261187","article-title":"Structural Analysis of Laplacian Spectral Properties of Large-Scale Networks","volume":"58","author":"Preciado","year":"2013","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_41","unstructured":"Karayel, E. (2023, December 29). Expander Graphs. Available online: https:\/\/www.isa-afp.org\/entries\/Expander_Graphs.html."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1287\/opre.12.3.450","article-title":"Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph","volume":"12","author":"Hakimi","year":"1964","journal-title":"Oper. Res."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1145\/261342.571216","article-title":"Approximation Algorithms for NP-Hard Problems","volume":"12","author":"Hochbaum","year":"1997","journal-title":"ACM Sigact News"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s10732-017-9345-x","article-title":"When a Worse Approximation Factor Gives Better Performance: A 3-Approximation Algorithm for the Vertex K-Center Problem","volume":"23","year":"2017","journal-title":"J. Heuristics"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"109228","DOI":"10.1109\/ACCESS.2019.2933875","article-title":"Approximation Algorithms for the Vertex K-Center Problem: Survey and Experimental Evaluation","volume":"7","author":"Lakouari","year":"2019","journal-title":"IEEE Access"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1145\/321906.321910","article-title":"On finding the maxima of a set of vectors","volume":"22","author":"Kung","year":"1975","journal-title":"J. ACM"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"399","DOI":"10.4153\/CJM-1956-045-5","article-title":"Maximal Flow through a Network","volume":"8","author":"Ford","year":"1956","journal-title":"Can. J. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A Note on Two Problems in Connexion with Graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Yu, X., Li, C., Zhang, J., and Letaief, K.B. (2019). Stochastic Geometry Analysis of Multi-Antenna Wireless Networks, Springer.","DOI":"10.1007\/978-981-13-5880-7"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/LWC.2018.2845377","article-title":"Downlink Coverage Probability in Cellular Networks with Poisson\u2014Poisson Cluster Deployed Base Stations","volume":"8","author":"Miyoshi","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Okabe, A., Boots, B., Sugihara, K., and Chiu, S.N. (2000). Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, John Wiley & Sons.","DOI":"10.1002\/9780470317013"}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/16\/2\/43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:49:53Z","timestamp":1760104193000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/16\/2\/43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,26]]},"references-count":51,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["fi16020043"],"URL":"https:\/\/doi.org\/10.3390\/fi16020043","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2024,1,26]]}}}