This paper introduces methods for the minimisation of virtual backbone size in wireless mesh networks, subject to practical constraints. The methods are centralised, which limits their usage to static applications. Four algorithms are presented, one exact and three heuristic. The exact method guarantees to find an optimal solution but runs in exponential time. Of the three heuristics, one is shown to match the performance of the optimal algorithm for all problem instances tested. The problem is constrained to introduce potentially massive levels of redundancy into the network topology, making the designs survivable
