Maritime Data Transmission Coverage Optimization Under Power and Distance Constraints

Abstract

A problem of the minimum-energy broadcast routing is considered for efficient maritime data transmission coverage. The power emitted by a ship radio station is limited, and this limitation tethers distance. Given an initial number of ships and their locations, they are triangulated. Upon the triangulation, the edges exceeding the maximum edge length equivalent to the maximum distance are removed. If the resulting graph has no disconnected ships, the solution is the minimum spanning tree. For two or more disconnected subgraphs, a minimum spanning tree is built for each of them, and the corresponding set of the efficient solutions is formed. Within this set, no minimum spanning tree exists that would either be shorter by connecting no fewer than a number of ships from an efficient solution or be not longer by connecting more than a number of ships from an efficient solution. The respective optimization problem, consisting in minimizing the broadcasting route length along with maximizing the number of ships communicating through the route, is solved by scalarizing the two criteria. The scalarization consists in standardizing the two criteria and calculating the distance of every achievable standardized efficient solution to the unachievable standardized solution. The percentage of two or more disconnected subgraphs is about 60%, whereas it is about 80% probable that the number of efficient solutions is equal to the number of disconnected subgraphs.