An efficient algorithm for relay placement in a ring sensor networks

This work proposes an intelligent algorithm which can arrange the minimum number of relays connecting n scattered base stations in a sensor networks with ring topology. The problem is firstly transformed to a corresponding problem of computing the shortest polygon connecting n base stations. Then a fleet of minimum number of relays can be deployed to cover the sides of the polygon. Algorithms are developed to construct such shortest polygon in polynomial time of O(kn  ) where 1⩽k⩽n1⩽k⩽n under a given computational threshold. Since these algorithms are fully polynomial time consuming, it is then efficient to be conducted in applications of relay placement or other computational geometric applications, such as tool path planning in layered manufacturing.