In this paper, we explore the problem of rendezvous of synchronous multi-robot systems. Each robot has its own unique, bounded yet controllable sensing range which can be adjusted. The state of those robots within the sensing range can be estimated, which induces the directed network topology of the multi-robot systems. In particular, we consider multi-robot systems containing faulty robots which can behave arbitrarily. Our recent work  has addressed the problem of achieving rendezvous in the presence of faulty robots under a restrictive class of conditions on network topology. In this work, we presented a theoretically correct, but computationally intractable algorithm. We extend our past work by proposing a new approximate algorithm that is computationally efficient, and by showing that the proposed algorithm solves our problem given faulty robots in general configurations under mild assumptions on the network topology. Thus, the main contribution of this paper is to provide an efficient computational framework and analysis of robust rendezvous algorithm in the presence of faulty robots. Several simulation results are provided to demonstrate that our algorithm performs well in the face of both stationary and dynamic faults.