## 2 Related Works
### The Topology Control Algorithms of RF-Based WSNs  
For improving the connectivity and the reliability of WSNs, in [6], the authors proposed a novel fuzzy-logic topology control (FTC) algorithm to achieve any desired average node degree by adaptively changing the transmission power. The FTC algorithm does not rely on location information of neighbors and is constructed from the training data set to facilitate the design process. In [7], for reducing energy consumption and end to end delay of WSNs, the authors proposed an optimization problem for energy consumption in WSNs, in which the topology control and the network-coding based multi-cast are combined together. This optimization problem is transformed into a convex problem which offers numerous theoretical and conceptual advantages. In this algorithm, the Karush-Kuhn-Tucker optimality conditions are presented to derive analytical expressions of the globally optimal solution. By these innovations, the performance of energy consumption and end to end delay was improved. In [8], the authors investigated a dynamic topology control scheme to improve the network lifetime for WSNs in the presence of selfish sensors, and propose a non-cooperative game-aided topology control approach to design energy-efficient and energy balanced network topologies dynamically. The nodes in the topology control game try to minimize their unwillingness to construct a connected network according to their residual energy and transmission power. In [9], considering the lossy links which can only provide probabilistic connectivity in network, the authors propose the probabilistic topology control (PTC). In PTC, the network connectivity is metered by network reachability and is defined as the minimal upper limit of the end-to-end delivery ratio between any pair of nodes in network. The PTC algorithm can find a minimal transmission power for each node while the network reachability is above a given application-specified threshold. The adaptive disjoint path vector (ADPV) algorithm has been proposed for heterogeneous WSNs in [10]. In ADPV, the algorithm is divided into two phases: single initialization phase and restoration phase. The restoration phase utilizes the alternative routes that are computed in the initialization phase with the help of a novel optimization algorithm which is based on the well-known set-packing problem. The simulation results demonstrate that the ADPV is superior in preserving super node connectivity. The authors in [11] consider that topology control has never achieved breakthroughs in real world deployment; moreover, the authors identify five practical obstacles of topology control algorithms at present. To address these obstacles, the authors propose a re-usable framework for implementation and evaluation of topology control. In [12] the authors propose the concept of a disjoint path vector (DPV) algorithm for a heterogeneous network in which the large number of sensor nodes have limited energy and computing capability and there are several supernodes with limited energy and unlimited computing capability. The DPV algorithm addresses the \(k\)-degree any-cast topology control problem where the main objective is to assign each sensor's transmission range such that each node has at least \(k\)-vertex-disjoint paths to super nodes and the total power consumption is minimized. The resulting topologies are tolerant up to \(k\)-\(1\) node failures in the worst case. In [13], to enhance the energy efficiency and reduce the radio interference in WSNs, the authors propose a new distributed topology control algorithm. In this algorithm, each node makes local decisions about its transmission power and the culmination of these local decisions produces a network topology that preserves global connectivity. The main idea of this topology control algorithm is the novel Smart Boundary Yao Gabriel Graph (SBYaoGG) and the appropriate optimizations to ensure that all links in network are symmetric and energy efficient.