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Since there is no fixed infrastructure or centralized management in wireless ad hoc networks (WANs), virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem [6]. Because the virtual backbone nodes need to carry other node's traffic and subject to failure, it is desirable to construct a fault tolerant virtual backbone. Most recent research has studied this problem in homogeneous networks. In this paper, we propose solutions for efficient construction of a fault-tolerant virtual backbone where the wireless nodes have different transmission ranges. Such a network can be modeled as a disk graph where any link between two nodes is either unidirectional or bidirectional. Since the graph is directed, we formulate the fault tolerant virtual backbone problem as a k- Strongly Connected m-Dominating and Absorbing Set problem (k-m-SCDAS). We first propose two heuristics, one to construct a 1-m-SCDAS and the other one to obtain a k-1-SCDAS in a directed graph. We next combine these two approaches to develop a general construction of k-m-SCDAS. Through extensive simulations, we compare the performance of these proposed algorithms.