## 1 Introduction  
Wireless sensor networks (WSNs) have a wide range of potential applications, including environment monitoring, military surveillance, and remote medical systems [1]. The energy-efficient routing has become a key issue attracting recent interest, since the battery of nodes is the most critical limiting factor [2; 3; 4; 5]. Power failure of a node affects its ability to forward the data packets of others as well as sending its own messages. Thus, the overall network lifetime will be seriously reduced. For this reason, extensive research has focused on how to prolong the network lifetime [6; 7; 8; 9; 10; 11; 12]. Much of the research on energy efficient routing for WSNs has several drawbacks. A single-hop clustering algorithm [13] can reduce energy consumption since only a fraction of the nodes, called cluster heads, communicate with the sink in one hop. However, a single-hop clustering algorithm is impractical, because nodes at a distance greater than one hop from the sink do not have adequate transmission power to communicate with the sink [14]. Although the multi-hop model would be a more practical approach to solve this problem, it can increase communication overhead and costs required to obtain the routing information in large-scale networks. In view of these issues, routing through a backbone reduces communication overhead and overall energy consumption for WSNs [15; 16; 17]. However, backbone nodes require extra functionality and therefore consume more energy compared with other nodes in the network. Unbalanced energy consumption among the sensor nodes may cause network partition and node failures where transmission from some sensors to the sink node becomes blocked. Therefore, construction of a stable backbone is one of the challenges in sensor network applications [2]. _Definition 1_ (\(d\)-hop cluster) - The \(d\)-hop cluster is the set of nodes that are at most \(d\) hops away from a cluster head. Each cluster has one cluster head and several cluster gateways and cluster members. Hierarchical Cluster-based Data Dissemination (HCDD) [18] applies a backbone construction algorithm for wireless ad hoc networks, such as Max-Min \(d\)-cluster [19], to WSNs. The Max-Min \(d\)-cluster diffuses node IDs to neighbors and each node selects the cluster head within a maximum \(d\)-hop to transmit data efficiently. Note that backbone construction for ad hoc networks is not considered energy consumption. Therefore, this scheme is inadequate for WSNs that are sensitive to energy. The residual energy in WSNs changes based on data transmission. Moreover, the degree of the node could decrease due to energy exhaustion. In the frequently changing network topology, we need to use a routing method that reflects the current network conditions, such as residual energy and degree, rather than using fixed node IDs. The Max-Min \(d\)-cluster forms clusters based on a pre-allocated ID, so there is a high probability of selecting the same node again as a cluster head when attempting to form new clusters. This characteristic decreases the transition overheads when old cluster heads give routing information to new cluster heads. However, the disadvantages are that the energy consumption of specific nodes increases since the same nodes are repeatedly selected. Therefore, in this paper, we present a novel algorithm to form a multi-hop cluster based stable backbone trees, called MCBT. This algorithm is appropriate for dynamic sensor networks by reflecting the network conditions such as residual energy and degree. It selects nodes with higher energy or degree as the cluster heads in order to prolong the network lifetime. Moreover, MCBT balances the energy consumption by distributing the packet transmission role among the nodes around the cluster head. This paper is organized as follows: in Section 2, the major routing techniques are introduced and discussed. Section 3 presents our stable backbone formation scheme for WSNs. The performance of MCBT is evaluated in Section 4.