In wireless sensor/ad hoc networks, all wireless nodes frequently flood the network channel by transmitting control messages causing “broadcast storm problem”. Thus, inspired by the physical backbone in wired networks, a Virtual Backbone (VB) in wireless sensor/ad hoc networks can help achieve efficient broadcasting. A well-known and well-researched approach for constructing virtual backbone is solving the Connected Dominating Set (CDS) problem. Furthermore, minimizing the size of the CDS is a significant research issue. We propose a new parallel scatter search algorithm with elite and featured cores for constructing a wireless sensor/ad hoc network virtual backbones based on finding minimum connected dominating sets of wireless nodes. Also, we addressed the problem of VB node/nodes failure by either deploying a previously computed VBs provided by the main pSSEF algorithm that does not contain the failed node/nodes, or by using our proposed FT-pSSEF algorithm repairing the broken VBs. Finally, as nodes in a VB incur extra load of communication and computation, this leads to faster power consumption compared to other nodes in the network. Consequently, we propose the virtual backbone scheduling algorithm SC-pSSEF which aims to find multiple VBs using the VBs provided by the pSSEF algorithm and switch between them periodically to prolong the network life time.