{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T02:03:44Z","timestamp":1774317824163,"version":"3.50.1"},"reference-count":69,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T00:00:00Z","timestamp":1736726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Navigatingdensely connected networks can be complex due to the different connection structures present within a network. No explicit algorithms are designed specifically for this navigation, so heuristic approaches and existing network systems are often employed. However, this task can become computationally asymmetrical, as the complexity of creating a representation of the city is lower than the complexity involved in identifying a set of feasible paths in a combinatorial order. This paper extends the applicability of morphological approaches to compute the shortest path in smart cities, driven by the complexity and size of the vital communication infrastructure. As is well known, this communication infrastructure changes dynamically, particularly with the evolving connection paths due to continuous population growth. Consequently, efficient communication trajectories can quickly become obsolete. The challenge of computing the best trajectories to respond more quickly to the growing population comes with high computational complexity. This paper presents an application that uses a discrete algorithm designed to compute the shortest path through a morphological approach. Specifically, it seeks to identify the best trajectory within a densely populated city based on a complex density graph. By incorporating morphological approaches into path-search algorithms, we can define a new family of methods that operate in discrete spaces with a morphological representation, resulting in approaches that have lower computational requirements. Other well-known applications in this context include the delivery of resources, such as managing electrical power consumption or minimizing time delays in resource delivery. This task is essential but classified as an NP problem, making it an appropriate scenario for applying the proposed algorithm to navigate a dense graph. The paper highlights the well-known problem of finding the shortest path as one of the potential applications of the introduced algorithm. The algorithm aims to identify the optimal path trajectory within a graph representing a dense city\u2019s real scenario. This discussion compares and contrasts the proposal with other established approaches, highlighting the advantages and characteristics of the proposed method.<\/jats:p>","DOI":"10.3390\/sym17010114","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T05:40:40Z","timestamp":1736746840000},"page":"114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Connecting Cities: A Case Study on the Application of Morphological Shortest Paths"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0444-9230","authenticated-orcid":false,"given":"Jorge L.","family":"Perez-Ramos","sequence":"first","affiliation":[{"name":"Faculty Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6635-5427","authenticated-orcid":false,"given":"Selene","family":"Ramirez-Rosales","sequence":"additional","affiliation":[{"name":"Faculty Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6543-5078","authenticated-orcid":false,"given":"Daniel","family":"Canton-Enriquez","sequence":"additional","affiliation":[{"name":"Faculty Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1519-105X","authenticated-orcid":false,"given":"Luis A.","family":"Diaz Jimenez","sequence":"additional","affiliation":[{"name":"Faculty Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-4566","authenticated-orcid":false,"given":"Herlindo","family":"Hernandez-Ramirez","sequence":"additional","affiliation":[{"name":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta No. 702, Desarrollo San Pablo, Santiago de Quer\u00e9taro 76125, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7711-9585","authenticated-orcid":false,"given":"Ana M.","family":"Herrera-Navarro","sequence":"additional","affiliation":[{"name":"Faculty Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0827-6645","authenticated-orcid":false,"given":"Hugo","family":"Jimenez-Hernandez","sequence":"additional","affiliation":[{"name":"Faculty Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, M., Xu, X., Yue, Q., and Wang, Y. (2021). A comprehensive survey and experimental comparison of graph-based approximate nearest neighbor search. arXiv.","DOI":"10.14778\/3476249.3476255"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, J., Wu, N., Zhao, W.X., Peng, F., and Lin, X. (2019, January 4\u20138). Empowering A* search algorithms with neural networks for personalized route recommendation. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330824"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Candra, A., Budiman, M.A., and Hartanto, K. (2020, January 16\u201317). Dijkstra\u2019s and a-star in finding the shortest path: A tutorial. Proceedings of the 2020 International Conference on Data Science, Artificial Intelligence, and Business Analytics (DATABIA), Medan, Indonesia.","DOI":"10.1109\/DATABIA50434.2020.9190342"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1108\/AEAT-11-2020-0272","article-title":"Regular graph-based free route flight planning approach","volume":"93","author":"Samolej","year":"2021","journal-title":"Aircr. Eng. Aerosp. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9015","DOI":"10.1007\/s10489-021-02303-8","article-title":"Novel best path selection approach based on hybrid improved A* algorithm and reinforcement learning","volume":"51","author":"Liu","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fang, Y., Huang, X., Qin, L., Zhang, Y., Zhang, W., Cheng, R., and Lin, X. (2020). A Survey of Community Search Over Big Graphs, Springer.","DOI":"10.1007\/s00778-019-00556-x"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Fan, D., and Shi, P. (2010, January 10\u201312). Improvement of Dijkstra\u2019s algorithm and its application in route planning. Proceedings of the 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery, Yantai, China.","DOI":"10.1109\/FSKD.2010.5569452"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s00521-017-2988-6","article-title":"Feature selection via a novel chaotic crow search algorithm","volume":"31","author":"Sayed","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s11704-018-7249-z","article-title":"Popular route planning with travel cost estimation from trajectories","volume":"14","author":"Liu","year":"2020","journal-title":"Front. Comp. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113572","DOI":"10.1016\/j.eswa.2020.113572","article-title":"Enhanced crow search algorithm for feature selection","volume":"159","author":"Ouadfel","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5448","DOI":"10.1109\/TIA.2021.3091418","article-title":"A Dijkstra-inspired graph algorithm for fully autonomous tasking in industrial applications","volume":"57","author":"Lotfi","year":"2021","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Liu, Y., Qi, N., Yao, W., Zhao, J., and Xu, S. (2020). Cooperative path planning for aerial recovery of a UAV swarm using genetic algorithm and homotopic approach. Appl. Sci., 10.","DOI":"10.3390\/app10124154"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"102493","DOI":"10.1016\/j.omega.2021.102493","article-title":"Algorithms based on branch and bound for the flying sidekick traveling salesman problem","volume":"104","author":"Montemanni","year":"2021","journal-title":"Omega"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, X., Tian, B., Hou, S., Li, X., Li, Y., Liu, C., and Li, J. (2023). Path Planning for Mount Robot Based on Improved Particle Swarm Optimization Algorithm. Electronics, 12.","DOI":"10.3390\/electronics12153289"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4378","DOI":"10.1016\/j.jfranklin.2023.01.033","article-title":"Dynamic path planning of mobile robot based on improved simulated annealing algorithm","volume":"360","author":"Shi","year":"2023","journal-title":"J. Frankl. Inst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.cie.2018.04.032","article-title":"Iterated local search algorithm with ejection chains for the open vehicle routing problem with time windows","volume":"120","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.ejor.2020.01.008","article-title":"A memory-based iterated local search algorithm for the multi-depot open vehicle routing problem","volume":"284","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7208","DOI":"10.1109\/TITS.2020.3003163","article-title":"A hybrid of deep reinforcement learning and local search for the vehicle routing problems","volume":"22","author":"Zhao","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_19","first-page":"2033","article-title":"Vehicle routing problem and related algorithms for logistics distribution: A literature review and classification","volume":"22","author":"Konstantakopoulos","year":"2022","journal-title":"Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Prajapati, V.K., Jain, M., and Chouhan, L. (2020, January 7\u20138). Tabu search algorithm (TSA): A comprehensive survey. Proceedings of the 2020 3rd International Conference on Emerging Technologies in Computer Engineering: Machine Learning and Internet of Things (ICETCE), Jaipur, India.","DOI":"10.1109\/ICETCE48199.2020.9091743"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.ins.2020.08.040","article-title":"GGA: A modified genetic algorithm with gradient-based local search for solving constrained optimization problems","volume":"547","author":"Palmieri","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"de Oliveira, G.C.R., de Carvalho, K.B., and Brand\u00e3o, A.S. (2019). A hybrid path-planning strategy for mobile robots with limited sensor capabilities. Sensors, 19.","DOI":"10.3390\/s19051049"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"20281","DOI":"10.1109\/ACCESS.2019.2897580","article-title":"An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem","volume":"7","author":"Deng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"92433","DOI":"10.1109\/ACCESS.2023.3302698","article-title":"Route planning for an autonomous robotic vehicle employing a weight-controlled particle swarm-optimized Dijkstra algorithm","volume":"11","author":"Sundarraj","year":"2023","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, L., Kan, J., Guo, J., and Wang, C. (2019). 3D Path planning for the ground robot with improved ant colony optimization. Sensors, 19.","DOI":"10.3390\/s19040815"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.ins.2019.03.070","article-title":"A hybrid ant colony optimization algorithm for a multi-objective vehicle routing problem with flexible time windows","volume":"490","author":"Zhang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"101507","DOI":"10.1016\/j.is.2020.101507","article-title":"A survey on graph-based methods for similarity searches in metric spaces","volume":"95","author":"Shimomura","year":"2021","journal-title":"Inf. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1109\/JAS.2019.1911405","article-title":"A memetic algorithm with competition for the capacitated green vehicle routing problem","volume":"6","author":"Wang","year":"2019","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/s40436-021-00366-x","article-title":"A bioinspired path planning approach for mobile robots based on improved sparrow search algorithm","volume":"10","author":"Zhang","year":"2022","journal-title":"Adv. Manuf."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Gaikwad, S.K., and Karwankar, A.R. (2019, January 23\u201325). Food image 3D reconstruction using image processing. Proceedings of the 2019 3rd International Conference on Trends in Electronics and Informatics (ICOEI), Tirunelveli, India.","DOI":"10.1109\/ICOEI.2019.8862615"},{"key":"ref_31","unstructured":"H\u00fftch, M., and Hawkes, P.W. (2020). Morphological Image Operators, Academic Press."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1080\/11663081.2019.1668678","article-title":"Logical dual concepts based on mathematical morphology in stratified institutions: Applications to spatial reasoning","volume":"29","author":"Aiguier","year":"2019","journal-title":"J. Appl. Non-Class. Log."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Roerdink, J.B. (2018). Mathematical morphology with noncommutative symmetry groups. Mathematical Morphology in Image Processing, CRC Press.","DOI":"10.1201\/9781482277234-7"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Preteux, F. (2018). On a distance function approach for gray-level mathematical morphology. Mathematical Morphology in Image Processing, CRC Press.","DOI":"10.1201\/9781482277234-10"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1137\/23M1598477","article-title":"Discrete morphological neural networks","volume":"17","author":"Marcondes","year":"2024","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Maragos, P. (2019). Tropical geometry, mathematical morphology and weighted lattices. Mathematical Morphology and Its Applications to Signal and Image Processing, Springer.","DOI":"10.1007\/978-3-030-20867-7_1"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Perez-Ramos, J.L., Ramirez-Rosales, S., Canton-Enriquez, D., Diaz-Jimenez, L.A., Xicotencatl-Ramirez, G., Herrera-Navarro, A.M., and Jimenez-Hernandez, H. (2024). Algorithm Based on Morphological Operators for Shortness Path Planning. Algorithms, 17.","DOI":"10.3390\/a17050184"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Dani, A.A.H., Supangkat, S.H., Lubis, F.F., Nugraha, I.G.B.B., Kinanda, R., and Rizkia, I. (2023). Development of a smart city platform based on digital twin technology for monitoring and supporting decision-making. Sustainability, 15.","DOI":"10.3390\/su151814002"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"104567","DOI":"10.1016\/j.scs.2023.104567","article-title":"Review on environmental aspects in smart city concept: Water, waste, air pollution and transportation smart applications using IoT techniques","volume":"94","author":"Salman","year":"2023","journal-title":"Sustain. Cities Soc."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Luckey, D., Fritz, H., Legatiuk, D., Dragos, K., and Smarsly, K. (2020, January 18\u201320). Artificial intelligence techniques for smart city applications. Proceedings of the 18th International Conference on Computing in Civil and Building Engineering: ICCCBE 2020, Sao Paolo, Brazil.","DOI":"10.1007\/978-3-030-51295-8_1"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"103979","DOI":"10.1016\/j.trd.2023.103979","article-title":"Road traffic noise monitoring in a Smart City: Sensor and Model-Based approach","volume":"125","author":"Pascale","year":"2023","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"109729","DOI":"10.1109\/ACCESS.2022.3213798","article-title":"State-of-the-art review on traffic control strategies for emergency vehicles","volume":"10","author":"Yu","year":"2022","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Liu, S., Li, Y., Fu, S., Liu, X., Liu, T., Fan, H., and Cao, C. (2022). Establishing a Multidisciplinary Framework for an Emergency Food Supply System Using a Modified Delphi Approach. Foods, 11.","DOI":"10.3390\/foods11071054"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.trpro.2021.02.072","article-title":"Transport services management on transport and logistic methods","volume":"54","author":"Sirina","year":"2021","journal-title":"Transp. Res. Procedia"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Silva, C.M., Silva, L.D., Santos, L.A., Sarubbi, J.F., and Pitsillides, A. (2018). Broadening understanding on managing the communication infrastructure in vehicular networks: Customizing the coverage using the delta network. Future Internet, 11.","DOI":"10.20944\/preprints201811.0294.v1"},{"key":"ref_46","first-page":"263","article-title":"Importance of road infrastructure in the economic development and competitiveness","volume":"18","author":"Ivanova","year":"2013","journal-title":"Econ. Manag."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2642","DOI":"10.1007\/s00453-022-00981-5","article-title":"Graph searches and their end vertices","volume":"84","author":"Rong","year":"2022","journal-title":"Algorithmica"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Rowold, M., \u00d6gretmen, L., Kerbl, T., and Lohmann, B. (2022). Efficient spatiotemporal graph search for local trajectory planning on oval race tracks. Actuators, 11.","DOI":"10.3390\/act11110319"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Chen, W., Zhang, Y., Xian, Y., and Wen, Y. (2023). Hotspot Information Network and Domain Knowledge Graph Aggregation in Heterogeneous Network for Literature Recommendation. Appl. Sci., 13.","DOI":"10.3390\/app13021093"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Gross, J.L., Yellen, J., and Anderson, M. (2018). Graph Theory and Its Applications, Chapman and Hall\/CRC.","DOI":"10.1201\/9780429425134"},{"key":"ref_51","unstructured":"IMCO (2024, December 14). \u00cdndice de Competitividad Urbana 2024. Available online: https:\/\/imco.org.mx\/indice-de-competitividad-urbana-2024\/."},{"key":"ref_52","unstructured":"Strutz, T. (2021). The distance transform and its computation. arXiv."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Les, T., Markiewicz, T., Dziekiewicz, M., and Lorent, M. (2020). Kidney boundary detection algorithm based on extended maxima transformations for computed tomography diagnosis. Appl. Sci., 10.","DOI":"10.3390\/app10217512"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Parveen, Z., Alam, M.A., and Shakir, H. (2017, January 8\u20139). Assessment of quality of rice grain using optical and image processing technique. Proceedings of the 2017 International Conference on Communication, Computing and Digital Systems (C-Code), Islamabad, Pakistan.","DOI":"10.1109\/C-CODE.2017.7918940"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Wang, H., Qi, X., Lou, S., Jing, J., He, H., and Liu, W. (2021). An efficient and robust improved A* Algorithm for path planning. Symmetry, 13.","DOI":"10.3390\/sym13112213"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Lewis, R. (2020). Algorithms for finding shortest paths in networks with vertex transfer penalties. Algorithms, 13.","DOI":"10.3390\/a13110269"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s10846-017-0748-6","article-title":"L* algorithm\u2014A linear computational complexity graph searching algorithm for path planning","volume":"91","author":"Niewola","year":"2018","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_58","unstructured":"Ruan, C., Luo, J., and Wu, Y. (2014, January 27\u201329). Map navigation system based on optimal Dijkstra algorithm. Proceedings of the 2014 IEEE 3rd International Conference on Cloud Computing and Intelligence Systems, Shenzhen, China."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s41651-019-0035-0","article-title":"Efficient Path Planning Method of USV for Intelligent Target Search","volume":"3","author":"Zhang","year":"2019","journal-title":"J. Geovisualization Spat. Anal."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Wang, J., Shang, X., Guo, T., Zhou, J., Jia, S., and Wang, C. (2019, January 2\u20134). Optimal path planning based on hybrid genetic-cuckoo search algorithm. Proceedings of the 2019 6th International Conference on Systems and Informatics (ICSAI), Shanghai, China.","DOI":"10.1109\/ICSAI48974.2019.9010519"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/j.ejor.2017.03.031","article-title":"A hybrid particle swarm optimization\u2013variable neighborhood search algorithm for constrained shortest path problems","volume":"261","author":"Marinakis","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1111\/cgf.14428","article-title":"Path Guiding Using Spatio-Directional Mixture Models","volume":"Volome 41","author":"Dodik","year":"2022","journal-title":"Computer Graphics Forum"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1007\/s11071-016-3284-1","article-title":"Gaussian mixture model and receding horizon control for multiple UAV search in complex environment","volume":"88","author":"Yao","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_64","first-page":"98","article-title":"Implementation Of Dijkstra\u2019s Algorithm In Determining The Shortest Path (Case Study: Specialist Doctor Search In Bandar Lampung)","volume":"3","author":"Gunawan","year":"2019","journal-title":"Int. J. Inf. Syst. Comput. Sci"},{"key":"ref_65","first-page":"012052","article-title":"AGV path planning based on improved Dijkstra algorithm","volume":"1746","author":"Sun","year":"2021","journal-title":"J. Physics: Conf. Ser."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"19761","DOI":"10.1109\/ACCESS.2021.3053169","article-title":"A new algorithm based on Dijkstra for vehicle path planning considering intersection attribute","volume":"9","author":"Zhu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_67","first-page":"1273","article-title":"Graph-based modeling and dijkstra algorithm for searching vehicle routes on highways","volume":"9","author":"Kirono","year":"2018","journal-title":"Int. J. Mech. Eng. Technol."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Gbadamosi, O.A., and Aremu, D.R. (2020, January 18\u201321). Design of a Modified Dijkstra\u2019s Algorithm for finding alternate routes for shortest-path problems with huge costs. Proceedings of the 2020 International Conference in Mathematics, Computer Engineering and Computer Science (ICMCECS), Lagos, Nigeria.","DOI":"10.1109\/ICMCECS47690.2020.240873"},{"key":"ref_69","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."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/114\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:27:45Z","timestamp":1759919265000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,13]]},"references-count":69,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["sym17010114"],"URL":"https:\/\/doi.org\/10.3390\/sym17010114","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,13]]}}}