## 2 Related Work  
A survey of energy conservation in WSNs is given in [4]. In order to efficiently reduce the energy consumption and further prolong the network lifetime, we focus on the literatures of energy conservation, especially those hierarchical protocols with concern on energy efficiency and data reduction schemes using data correlation and prediction. Certainly, the hierarchical architecture is introduced to WSNs because it has proven to be an effective approach to provide better energy efficiency. As network nodes are organized in clusters, the router nodes are responsible for coordinating activities within the cluster and forwarding data readings between clusters. The use of routing hierarchy has many advantages, including better energy efficiency and scalability. LEACH (Low Energy Adaptive Clustering Hierarchy) [22] is the most famous algorithm that uses clustering to prolong the network lifetime. From the energy perspective, it uses randomized rotation of the cluster heads to distribute the energy consumption among the sensor nodes in a network. Many research efforts in energy efficiency follow LEACH with different concerns, such as cluster head selection, clustering cost, and cluster maintenance. In [23], the authors propose an improved routing algorithm of ring based multi-hop clustering (IRBMC) to prolong the lifetime of network. WSNs are divided into heterogeneous spacing rings to control the cluster number and build unequal size of clusters in different rings. The cluster heads selection is depending on the residual average energy estimation, which is taken into account to balance energy consumption of nodes in each ring. Also, in [24], two integer linear program (ILP) formulations are proposed for assigning sensor nodes to clusters in a two-tiered network where the relay nodes are used as cluster heads. The objective of ILP formulations is to load balanced clustering, that is, to maximize the lifetime of the relay node network by distributing the total load for data communication over the different relay nodes. Data reduction techniques are designed to reduce the amount of transmissions, including data aggregation [25, 26], compression, and prediction [16, 17]. In [26], the authors propose a data correlation-based clustering (DCC). In each round of data acquisition, data readings of all nodes in one cluster are gathered at the cluster head, on which data readings will be compressed before send to the sink. The sink mines data correlations from historical data to construct clusters. However, the network is divided into several disjoint clusters by minimum degree first clustering, which is irrelevant with data correlation. That is, the data correlation between the cluster members can't be substantiated. In [16], PREMON paradigm trades increased computation (for deriving prediction models) for savings in number transmissions. In [17], the authors propose a buddy protocol that sensor nodes with high temporal correlation formed a buddy group. The nodes within the same buddy group (cluster) take turns keeping their radio on. The representative node responds on behalf of its buddies. However, GAF [27] is used for clustering in this protocol and the data readings between buddies have not been verified as being correlated. Therefore, the difference of data readings between the representative and buddies is not negligible. In [25], the authors propose a distributed clustering-based aggregation algorithm for spatially correlated WSNs. When the clusters are constructed by the \(\alpha\)-local spatial clustering, the data readings of cluster head and members have very high correlation. Only the cluster heads need to do the data sampling work. The data readings are then aggregated to a cluster head backbone and transmitted to the sink. Due to the lack of re-clustering mechanism, the constructed clusters based on weighteddominant set cannot accommodate themselves to the changing environment. Further, the cluster head has to keep sensing in order to monitor environment.