## 4 Algorithmic Approaches
The goal is to find a balance that allows us to provide optimal service for users while ensuring operational feasibility conditions. Conceptualization, A.V., P.A., and A.D.F. ; methodology, A.V., P.A., and A.D.F. ; software, A.V. and P.A. ; validation, A.V., P.A., and A.D.F. ; formal analysis, A.V., P.A., A.D.F., and E.S.J. ; investigation, A.V., P.A., A.D.F., and E.S.J. ; resources, A.V., P.A., A.D.F., and E.S.J. ; data curation, A.V., P.A., and A.D.F. ; writing-original draft preparation, A.V. and P.A. ; writing-review and editing, A.V., P.A., A.D.F., and E.S.J. ; visualization, A.V., P.A., A.D.F., and E.S.J. ; supervision, P.A., A.D.F., and E.S.J. ; project administration, P.A. and A.D.F. ; funding acquisition, P.A. and A.D.F. All authors have read and agreed to the published version of the manuscript. The authors acknowledge the financial support from Projects Dicyt 062313 AS, ANID/FONDECYT Iniciacion No. 11230129, and the Competition for Research Regular Projects, year 2021, code LPR21-02; Universidad Tecnologica Metropolitana. The dataset is available upon request from the authors. The raw data supporting the conclusions of this article will be made available by the authors upon request. The authors acknowledge the support of the Vicerrectoria de Investigacion, Innovacion y Creacion (VRIIC) of the Universidad de Santiago de Chile. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} SDN & Software-defined network \\ QoS & Quality of service \\ IoUT & Internet of underwater things \\ CASM & Multi-controller balancing strategy \\ SQAR & Routing protocol adaptative \\ CAMD & Controller adaption and migration decision \\ DALB & Dynamic and adaptive load balancing \\ VLAN & virtual local area network \\ TSSDN & Time-sensitive software-defined networking \\ TSN & Time-sensitive networking \\ IIoT & Industrial internet of things applications \\ FRER & Frame replication and elimination for reliability \\ \(G=(V,A)\) & Graph with a set of nodes, \(V\), and a set of arcs, \(A\) \\ NC & Number of controllers \\ \end{tabular} 

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