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In mobile ad-hoc networks, hosts communicate with each other without the help of any physical infrastructure. Inevitably, the communication tends to be less efficient in terms of computational and communicational overhead. Recent studies have shown that virtual backbone can help reduce the communication overhead. However, the backbone structure is very vulnerable due to several reasons, e.g., node mobility and unstable links, etc. In this paper, we introduce a localized virtual backbone construction scheme, connected maximal independent set with multiple initiators (MCMIS), which takes node stability into consideration and can construct the backbone quickly. We design MCMIS aiming at three goals: small backbone size, fast construction, stable backbone. Through extensive simulations, we find that our scheme could obtain a better performance on stability and backbone size than other localized schemes.