{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:19Z","timestamp":1760240659478,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T00:00:00Z","timestamp":1566777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>The need for smart and sustainable communication systems has led to the development of mobile communication networks. In turn, the vast functionalities of the global system of mobile communication (GSM) have resulted in a growing number of subscribers. As the number of users increases, the need for efficient and effective planning of the \u201climited\u201d frequency spectrum of the GSM is inevitable, particularly in densely-populated areas. As such, there are ongoing discussions about frequency (channel) allocation methods to resolve the challenges of channel allocation, which is a complete NP (Nondeterministic Polynomial time) problem. In this paper, we propose an algorithm for channel allocation which takes into account soft constraints (co-channel interference and adjacent channel interference). By using the Manhattan distance concept, this study shows that the formulation of the algorithm is correct and in line with results in the literature. Hence, the Manhattan distance concept may be useful in other scheduling and optimization problems. Furthermore, this unique concept makes it possible to develop a more sustainable telecommunication system with ease of connectivity among users, even when several subscribers are on a common frequency.<\/jats:p>","DOI":"10.3390\/fi11090186","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T10:54:53Z","timestamp":1566816893000},"page":"186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sustainable Communication Systems: A Graph-Labeling Approach for Cellular Frequency Allocation in Densely-Populated Areas"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6914-0488","authenticated-orcid":false,"given":"Adebola","family":"Orogun","sequence":"first","affiliation":[{"name":"Department of Computer Science, Faculty of Science, Adekunle Ajasin University, Akungba 234034, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8369-4471","authenticated-orcid":false,"given":"Oluwaseun","family":"Fadeyi","sequence":"additional","affiliation":[{"name":"Department of Geology, Faculty of Geography and Geoscience, University of Trier, Universit\u00e4tsring 15, 54296 Trier, Germany"},{"name":"Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, Rokitanskeho 62, Hradec Kralove 50003, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5992-2574","authenticated-orcid":false,"given":"Ondrej","family":"Krejcar","sequence":"additional","affiliation":[{"name":"Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, Rokitanskeho 62, Hradec Kralove 50003, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,26]]},"reference":[{"key":"ref_1","first-page":"8","article-title":"Development of Models for Managing Network Congestion on Global System for Mobile Communication (GSM) in Nigeria","volume":"1","author":"Kuboye","year":"2011","journal-title":"J. Wirel. Netw. Commun."},{"key":"ref_2","unstructured":"Haider, B., Zafrullah, M., and Islam, M.K. (2009, January 20\u201322). Radio Frequency Optimization & QoS Evaluation in Operational GSM Network. Proceedings of the world Congress on Engineering and Computer Science, San Francisco, CA, USA."},{"key":"ref_3","first-page":"135","article-title":"Algorithms for Solving Frequency Assignment Problem in Wireless Networks","volume":"Volume 513","author":"Badica","year":"2014","journal-title":"Recent Developments in Computational Collective Intelligence"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dcan.2015.02.001","article-title":"The challenges of M2M massive access in wireless cellular networks","volume":"1","author":"Biral","year":"2015","journal-title":"Digit. Commun. Netw."},{"key":"ref_5","first-page":"2","article-title":"NB-IoT: A sustainable technology for connecting billions of devices","volume":"4","author":"Westerberg","year":"2016","journal-title":"Ericsson Technol. Rev."},{"key":"ref_6","first-page":"3479246","article-title":"A Geometric Method for Estimating the Nominal Cell Range in Cellular Networks","volume":"2018","author":"Garcia","year":"2018","journal-title":"Mob. Inf. Syst."},{"key":"ref_7","unstructured":"Mouly, M., and Pautet, M.B. (2019, August 21). The GSM System for Mobile Communications. Available online: https:\/\/dl.acm.org\/citation.cfm?id=573838."},{"key":"ref_8","unstructured":"Hamad-Ameen, J.J. (2008, January 27\u201330). Frequency Planning in GSM Mobile. Proceedings of the TELE-INFO\u201908 Proceedings of the 7th WSEAS International Conference on Telecommunications and Informatics, Istanbul, Turkey."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Xu, Y., and Sakho, I. (2015). Frequencies Assignment in Cellular Networks. Intelligent Information and Database Systems, Springer.","DOI":"10.1007\/978-3-319-15702-3_21"},{"key":"ref_10","unstructured":"Rughooputh, S., Coomar, H., and Cheeneebash, J. (2014). A Comprehensive Review of Methods for the Channel Allocation Problem, African Minds."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13673-016-0075-0","article-title":"Evaluation of a channel assignment scheme in mobile network systems","volume":"6","author":"Nurelmadina","year":"2016","journal-title":"Hum.Centric Comput Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1109\/TBC.2002.806793","article-title":"New modeling approach to the frequency assignment problem in broadcasting","volume":"48","author":"Idoumghar","year":"2002","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Gozupek, D., Genc, G., and Ersoy, C. (2009, January 23). Channel assignment problem in cellular networks: A reactive tabu search approach. Proceedings of the 2009 24th International Symposium on Computer and Information Sciences, Guzelyurt, Cyprus.","DOI":"10.1109\/ISCIS.2009.5291830"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/COMST.2000.5340800","article-title":"Channel assignment schemes for cellular mobile telecommunication systems: A comprehensive survey","volume":"3","author":"Katzela","year":"1996","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_15","unstructured":"Peng, Y., Wang, L., and Soong, B.H. (2003, January 7\u201310). Optimal channel assignment in cellular systems using tabu search. Proceedings of the 14th IEEE Proceedings on Personal, Indoor and Mobile Radio Communications, Beijing, China."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bertossi, A.A., Pinotti, C.M., and Tan, R.B. (2000, January 11). Efficient Use of Radio Spectrum in Wireless Networks with Channel Separation Between Close Stations. Proceedings of the 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communication, Boston, MA, USA.","DOI":"10.1145\/345848.345853"},{"key":"ref_17","unstructured":"(2019, August 21). Tech Republic, Hybrid Channel Allocation in Wireless Cellular Networks. Available online: https:\/\/www.techrepublic.com\/resource-library\/whitepapers\/hybrid-channel-allocation-in-wireless-cellular-networks."},{"key":"ref_18","unstructured":"Davis, J.S. (2019, August 21). Channel Allocation. Available online: http:\/\/www.wirelesscommunication.nl\/reference\/chaptr04\/cellplan\/dca.htm."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1023\/A:1019196321628","article-title":"A new localized channel sharing scheme for cellular networks","volume":"5","author":"Li","year":"1999","journal-title":"Wirel. Netw."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00354875","article-title":"Channel assignment in cellular radio using genetic algorithms","volume":"3","author":"Kim","year":"1996","journal-title":"Wirel. Pers. Commun."},{"key":"ref_21","unstructured":"Duran, M. (2019, August 21). How to Unlock Your Phone\u2019s Trusty Call-Blocking Powers. Available online: https:\/\/www.wired.com\/2016\/07\/unlock-phones-trusty-call-blocking-powers\/."},{"key":"ref_22","unstructured":"Acampora, A.S. (2013). An Introduction to Broadband Networks: LANs, MANs, ATM, B-ISDN, and Optical Networks for Integrated Multimedia Telecommunications, Springer Science & Business Media."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1016\/j.jare.2014.10.008","article-title":"New hybrid frequency reuse method for packet loss minimization in LTE network","volume":"6","author":"Ali","year":"2015","journal-title":"J. Adv. Res."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jiang, F., Wang, H., Ren, H., and Xu, S. (2017). Energy-efficient resource and power allocation for underlay multicast device-to-device transmission. Future Internet, 9.","DOI":"10.3390\/fi9040084"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/25.312777","article-title":"Generalized fixed channel assignment in microcellular communication systems","volume":"43","author":"Chu","year":"1994","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.engappai.2014.11.001","article-title":"A combined negative selection algorithm-particle swarm optimization for an email spam detection system","volume":"39","author":"Idris","year":"2015","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yin, L., Li, X., Lu, C., and Gao, L. (2016). Energy-efficient scheduling problem using an effective hybrid multi-objective evolutionary algorithm. Sustainability, 8.","DOI":"10.3390\/su8121268"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.3233\/JIFS-169133","article-title":"Fuzzy granular classifier approach for spam detection","volume":"32","author":"Salehi","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_29","unstructured":"Lim, K.C., Selamat, A., Zabil, M.H.M., Selamat, M.H., Alias, R.A., Puteh, F., Mohamed, F., Krejcar, O., Herrera-Viedma, E., and Fujita, H. (2018, January 26\u201328). Feasibility comparison of HAC algorithm on usability performance and self-reported metric features for MAR learning. Proceedings of the 17th International Conference on New Trends in Intelligent Software Methodology Tools and Techniques (SoMeT 2018), Granada, Spain."},{"key":"ref_30","first-page":"931256","article-title":"A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications","volume":"2015","author":"Zhang","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_31","unstructured":"B\u00e4ck, T., and Hoffmeister, F. (1991, January 13\u201316). Extended Selection Mechanisms in Genetic Algorithms. Proceedings of the Fourth International Conference on Genetic Algorithms, San Diego, CA, USA."},{"key":"ref_32","unstructured":"Shao, Z. (2019, August 21). The Research on the L(2,1)-labeling problem from Graph theoretic and Graph Algorithmic Approaches. Available online: https:\/\/ir.lib.uwo.ca\/cgi\/viewcontent.cgi?article=1604&context=etd."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1162\/coli.2010.36.1.36101","article-title":"A Graph-theoretic Framework for Semantic Distance","volume":"36","author":"Tsang","year":"2010","journal-title":"Comput. Linguist."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/S0166-218X(02)00597-8","article-title":"Computing graph invariants on rotagraphs using dynamic algorithm approach: the case of (2,1)-colorings and independence numbers","volume":"129","author":"Klavzar","year":"2003","journal-title":"Discrete Appl. Math."},{"key":"ref_35","unstructured":"Read, R.C. (1972). Graph Coloring Algorithm. Graph Theory and Computing, Academic Press."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wigderson, A. (1982, January 5\u20137). A New Approximate Graph Coloring Algorithm. Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, San Francisco, CA, USA.","DOI":"10.1145\/800070.802207"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Middleton, W.M., and Van Valkenburg, M.E. (2002). Chapter 46: Cellular Telecommunications Systems. Reference Data for Engineers, Newnes. [9th ed.].","DOI":"10.1016\/B978-075067291-7\/50048-0"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1294133","DOI":"10.1080\/23311916.2017.1294133","article-title":"Interference management techniques in cellular networks: A review","volume":"4","author":"Adediran","year":"2017","journal-title":"Cogent Eng."},{"key":"ref_39","unstructured":"Horalek, J., Sobeslav, V., Krejcar, O., and Balik, L. Communications and security aspects of smart grid networks design. Proceedings of the International Conference on Information and Software Technologies."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Wu, T.T., Gennari, R., Huang, Y.M., Xie, H., and Cao, Y. (2017). Social network sites and their use in education. Emerging Technologies for Education, Springer.","DOI":"10.1007\/978-3-319-52836-6"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Hruska, J., and Maresova, P. (2019). Design of business canvas model for social media. Emerging Technologies in Data Mining and Information Security, Springer.","DOI":"10.1007\/978-981-13-1498-8_6"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s00779-015-0856-x","article-title":"Information and communications technologies for elderly ubiquitous healthcare in a smart home","volume":"19","author":"Deen","year":"2015","journal-title":"Pers. Ubiquitous Comput."},{"key":"ref_43","unstructured":"Rezny, L., White, J.B., and Maresova, P. (2019, August 21). The knowledge economy: Key to sustainable development?. Available online: https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0954349X18302200."},{"key":"ref_44","first-page":"124549","article-title":"Anti-k-labeling of graphs","volume":"363","author":"Guan","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Pan, X., Gao, L., Zhang, B., Yang, F., and Liao, W. (2018). High-Resolution Aerial Imagery Semantic Labeling with Dense Pyramid Network. Sensors, 18.","DOI":"10.3390\/s18113774"}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/9\/186\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:14:03Z","timestamp":1760188443000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/9\/186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,26]]},"references-count":45,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["fi11090186"],"URL":"https:\/\/doi.org\/10.3390\/fi11090186","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2019,8,26]]}}}