We propose a notion of extended dominating set where each node in an ad hoc network is covered by either a dominating neighbor or several 2-hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks whereby transmitting independent copies of a packet generates diversity and combats the effects of fading. We first show the NPcompleteness of the minimum extended dominating set problem. Then, several heuristic algorithms, global and local, for constructing a small extended dominating set are proposed. These are non-trivial extensions of the existing algorithms for the regular dominating set problem. The application of the extended dominating set in efficient broadcasting is also discussed. The performance analysis includes an analytical study in terms of approximation ratio and a simulation study of the average size of the extended dominating set derived from the proposed algorithms.
Recently, the use of a virtual backbone in various applications in mobile ad hoc networks (MANETs) has become popular. These applications include topology management, point and area coverage, and routing protocol design. In a MANET, one challenging issue is to construct a virtual backbone in a distributed and localized way while balancing several conflicting objectives: small approximation ratio, fast convergence, and low computation cost. Many existing distributed and localized algorithms select a virtual backbone without resorting to global or geographical information. However, these algorithms incur a high computation cost in a dense network. In this paper, we propose a distributed solution based on reducing the density of the network using two mechanisms: clustering and adjustable transmission range. By using adjustable transmission range, we also achieve another objective, energy-efficient design, as a by-product. As an application, we show an efficient broadcast scheme where nodes (and only * This work was supported in part by NSF grants CCR 0329741, CNS 0434533, CNS 0422762, and EIA 0130806. 1 nodes) in a virtual backbone are used to forward the broadcast message. The virtual backbone is constructed using Wu and Li's marking process [37] and the proposed density reduction process. The application of the density reduction process to other localized algorithms is also discussed. The efficiency of our approach is confirmed through both analytical and simulation study.keywords: Adjustable transmission range, broadcasting, clustering, connected dominating set (CDS), energy efficiency, mobile ad hoc networks (MANETs).
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