# Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network
## 1 Introduction
The criticality index is the summation of node's neighbor dissimilarity ratios. According to this index, a node is deemed as the high criticality node if it not only has many neighbors, but also is one of the few bridge nodes among its neighbors. In this paper, a mobile charger is employed to charge the sensor nodes in WRSN. Due to the limited travel distance of the mobile charger, it can only serve a part of nodes during a single charging tour. The uncharged node will enter into a sleep mode when its battery is depleted and then wakes up  
Figure 1: Example of high criticality nodes. after it gets charged. If the high criticality nodes become inactive, the network may suffer data loss. Therefore, in order to mitigate data loss in the network, we formulate an optimization problem with the objective of maximizing the sum of criticality indexes of nodes to be charged, subject to the mobile charger's traveling distance constraint. Then, we propose a heuristic algorithm to solve this problem. The main contributions of this paper are summarized as follows:  
* To the best of our knowledge, this is the first work to consider the node's disjointed state in the mobile charger scheduling problem. Compared to the state-of-arts, we distinguish the inactive nodes into two groups, the sleep nodes whose energy is exhausted and the disjointed nodes which are active but can't send data to the base station via any available routing path. Most existing works only consider how to decrease the sleep node's nonfunctional time with the help of a mobile charger, but ignore the disjointed node's data loss. In our work, to maintain network connectivity as long as possible and mitigate the data loss, we consider reducing the inactive time of both sleep nodes and disjointed nodes via the mobile charger with limited charging ability. * We introduce a metric called the criticality index to quantify the node's criticality, which indicates a node's contribution to network connectivity. It measures the dissimilarity between the node's neighboring set and its neighbors' neighboring sets. A node has a higher index if it plays a more important role as a bridge between two or more node sets. In addition, energy criticality is also considered, which indicates a node's consumed energy ratio and can be used to measure the node's desire for charging. We use this ratio to weight the criticality index to reduce the possibility of charging the full energy nodes. Otherwise, some higher criticality nodes will always be selected to be charged even if they have a great amount of residual energy. * We formulate the charging scheduling problem as a novel optimization problem, with an objective of maximizing the total criticality indexes of nodes selected in the charging tour and subject to the mobile charger's traveling distance constraint. To solve this NP-hard problem, we propose a heuristic algorithm. The heuristic algorithm includes three steps, which are spanning tree growing, tour construction, and tour improvement. The rest of the paper is organized as follows. Section 2 gives brief overviews of the literature. In Section 3, we introduce the system model and define the problems. Section 4 proposes the heuristic algorithm for the charging scheduling problems. In Section 5, we conduct some simulations to compare the proposed algorithm with a state-of-art scheduling algorithm Nearest-Job Next with Preemption and a traditional Travel-Salesman-Problem based algorithm. Finally, we conclude this paper in Section 6.