# PDTR: Probabilistic and Deterministic Tree-based Routing for Wireless Sensor Networks
## 1 Introduction  
A wireless sensor network (WSN) is a network of low-power and low-cost devices that communicate among themselves within the communication range using radio signals. Many protocols have been proposed to maximize both energy efficiency and energy balancing. WSNs have generated an increasing interest because of their significant role in our daily lives: i.e., surveillance, health care, acoustic and seismic detection, environmental monitoring. Most of these protocols are location-based schemes, characterized by three facts: first, each node in the network must be aware of its location information. Second, each node must be aware of its direct neighbor node's location. Third, the source node must be aware of the destination node's location [1]. The localization of WSNs is a very crucial issue; many methods have been proposed to get the node's location, and most of these proposed methods supposed that only a small proportion of sensor nodes, called anchor (beacon) nodes, are location-aware through a global positioning system (GPS), because of the high cost and energy consumption of GPS. However, the other nodes could obtain their position by estimating distance, using the anchor nodespositions, through other localization technologies [2; 3]. Other proposed WSN localization technologies are based on different measurement techniques such as the time-of-arrival (TOA), angle-of-arrival (AOA), and received signal strength indicator (RSSI) [4; 5; 6; 7]. Later, in [8; 9], the cooperative localization technology was developed for hybrid networks containing mobile and static sensors. Recently, in [10], the authors proposed a centralized expectation maximization-based passive localization technology for asynchronous receivers (EMpILaR). Being aware of the nodes' location allows the use of many power control techniques to reduce energy consumption. Data forwarding toward the sink via deterministic protocols may cause quick energy depletion for some nodes, due to the sender node's forwarder unique choice, which causes a topology disruption, thus a quick network death. Meanwhile, the probabilistic routing approach came with the improvement, such that each sensor has to select its forwarder from a set of its candidates according to their routing probabilities, based on its neighborhood knowledge, thus providing a longer network lifetime. From the existing probabilistic and deterministic protocols, we concluded that to minimize the energy consumption and prolong the network lifetime, the protocol should depend on three factors. Reference [11] proposed a Hop-based Routing Protocol based on an Energy Efficient Minimum Spanning Tree for WSN. From the simulation results, it was proved that the proposed protocol improved the network in terms of energy consumption and lifetime extension, hence the importance of the hop-count factor. Article [12] also considered this factor in the presented protocol called (STDD). The authors in [13] showed that the Euclidian distance has a direct effect on energy consumption--the more the distance is minimized, the more the consumed energy is reduced. In [5; 6], a p-persistence protocol was proposed, such that the forwarding probability is calculated according to the distance between two nodes. Thus, it uses the relative distance between two nodes for retransmission delay adjustment. Thus, the importance of the transmission distance factor is shown. In WSNs, ensuring energy efficiency does not mean ensuring energy balancing. Hence, to balance the energy dissipation, the selection of the routing protocol should be performed to save the residual energy in each node, as much as possible. Article [14] proposed a Distance-based Energy-Aware Routing (DEAR) algorithm. It ensures energy efficiency, energy balancing, and takes into consideration two factors: distance and residual energy. DEAR simulation provided better results in terms of energy balancing and consumption.