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It is well-known that placing disks in the triangular lattice pattern is optimal for achieving full coverage on a plane. With the emergence of wireless sensor networks, however, it is now no longer enough to consider coverage alone when deploying a wireless sensor network; connectivity must also be con-sidered. While moderate loss in coverage can be(More)
—In this paper, we study deployment patterns to achieve full coverage and k-connectivity (k ≤ 6) under different ratios of the sensor communication range (denoted by Rc) to the sensing range (denoted by Rs) for homogeneous wireless sensor networks (WSNs). In particular, we propose new patterns for 3-and 5-connectivity. We also discover that there exists a(More)
—In wireless sensor networks, multiple-coverage, in which each point is covered by more than one sensor, is often required to improve detection quality and achieve high fault tolerance. However, finding optimal patterns that achieve multiple-coverage in a plane remains a long-lasting open problem. In this paper, we first derive the optimal deployment(More)
In this paper, we propose deployment patterns to achieve full coverage and three-connectivity, and full coverage and five-connectivity under different ratios of sensor communication range (denoted by Rc) over sensing range (denoted by Rs) for wireless sensor networks (WSNs). We also discover that there exists a hexagon-based universally elemental pattern(More)
—We study the issue of optimal deployment to achieve four connectivity and full coverage for wireless sensor networks (WSNs) under different ratios of sensors' communication range (denoted by r c) to their sensing range (denoted by rs). We propose a " Diamond " pattern, which can be viewed as a series of different evolving patterns. When r c/rs ≥ √ 3, the(More)
In this paper, we study the optimal deployment pattern problem in wireless sensor networks (WSNs). We propose a new set of patterns, particularly when sensors' communication range (<i>r<inf>c</inf></i>) is relatively small compared to their sensing range (<i>r<inf>s</inf></i>), and prove their optimality. In this study, we discover an interesting(More)
—In this paper, we study optimal deployment in terms of the number of sensors required to achieve four-connectivity and full coverage under different ratios of sensors' communication range (denoted by r c) to their sensing range (denoted by r s). We propose a new pattern, the Diamond pattern, which can be viewed as a series of evolving patterns. When r c =r(More)
Keywords: Covering-based rough set Covering lower (upper) approximation Point-set topology Neighborhood a b s t r a c t In this paper, we study the axiomatic issue of a type of covering upper approximation operations. This issue was proposed as an open problem. We also further some known results by using only a single covering approximation operator to(More)
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