## 3 Dynamic Sensor Scheduling Algorithms
### Centralized Adaptive Scheduling Algorithm (CASA)  
There are many possible data gathering strategies to accomplish the sensing tasks. In many applications, the monitored area may be used to determine the group members in a specific round. For instance, since the core sensing field is covered by the sensing area of 1-hop cluster members in the cluster-based topology, the round determination problem can be expressed by the coverage subject to the number of 1-hop cluster members covered in the round sensing area,  
\[\min_{i\in RG_{\ell}}\ \ \bigcup O_{i} \tag{2}\]  
subject to: \(i,j\in RG_{\ell},j\
otin S_{b}^{(i)},((\cup H_{1}(i)+RG_{\ell})\cap H_{1})=H_{1}\), where \(O_{i}\) represents the coverage overlap of sensor \(i\) with other round group members, \(H_{1}(i)\) is the set of neighboring 1-hop cluster members of sensor \(i\), \(RG_{\ell}\) is the set of round group members of round \(\ell\), sensors \(i\) and \(j\) belong to the set of round group members \(RG_{\ell}\), \(H_{1}\) is the set of 1-hop cluster members, and \(S_{b}^{(i)}\) is the set of neighboring sensors of sensor \(i\). The rationale for using the constraint in (2) is to avoid heavy overlap between sensors in the same round. However, without location information, it may be not easy to cover the desired area and minimize the coverage overlap in each round. Hence, the optimization of the coverage may be modified to satisfy the problem constraint by the following scheme. The Scheduling Scheme  
When developing the sensing schedule, two rounds of local flooding are initiated in order to gather topology information for the clusterhead in the 2-hop cluster structure. Hence, given the local information such as neighboring connectivity, a clusterhead may choose a 2-hop cluster member and a 1-hop relay node to initialize the proposed scheduling algorithm. After that, the clusterhead may randomly pick 1-hop cluster members, which have no communication links with the chosen group members, as the new round group members. The purpose for this selection policy is to reduce the overlap between group members in the same round. Note that the relay node can be selected as the group member in the following round since it is not responsible for sensing at this round. If all the 2-hop cluster members have been selected for initializing the sensing rounds, the clusterhead will select a 1-hop cluster member for starting the new round. This procedure is repeated until all of the cluster members have been assigned. Then,with a common local clock time in the cluster, the clusterhead triggers two rounds of 1-hop flooding for broadcasting the sensor scheduling information throughout the 2-hop cluster topology. Observe that the overlap is only approximately minimized; in our experiments we have noticed that the answers tend to be close to the optimal. The pseudo-code of the proposed algorithm is presented in Table 1, where \(H_{1}(m)\) is the set of neighboring 1-hop cluster members of sensor \(m\) in a cluster, \(H_{2}(n)\) is the set of neighboring 2-hop cluster members of sensor \(n\) in a cluster, \(RG_{\ell}\) is the set of round group members of round \(\ell\), \(U\) is the set of cluster members, \(H_{1}\) and \(H_{1}^{{}^{\prime}}\) are the sets of 1-hop nodes, \(H_{2}\) is the set of 2-hop nodes, and \(N_{RG}\) is the number of sensing rounds in a cluster.