## 5 Analysis of Prominent Clustering Routing Protocols in WSNs
### Data-Transmission Based Clustering Routing Protocols
#### 5.2.6 Hgmr  
Hierarchical Geographic Multicast Routing (HGMR), proposed in [31] by [PERSON] _et al._, is a location-based multicast protocol. This protocol seamlessly incorporates the key design concepts of the Geographic Multicast Routing (GMR) [78] and Hierarchical Rendezvous Point Multicast (HRPM) protocols [79], and optimizes them by providing forwarding energy efficiency as well as scalability to large-scale WSNs.  
HGMR starts with a hierarchical decomposition of a multicast group into subgroup of manageable size by means of the key concept of mobile geographic hashing of HRPM. Within each subgroup, HGMR adopts the local multicast scheme of GMR to forward data packets along multiple branches of the multicast tree in one transmission. In HGMR, the multicast group is divided into subgroups using the mobile geographic hashing idea: the deployment area is recursively partitioned into a number of \(d^{2}\) equal-sized square sub-domains called cells, where \(d\) is decomposition index depending on the encoding overhead constraints, and each cell comprises a manageably-sized subgroup of members. In each cell there is an Access Point (AP) responsible for all members in that cell, and all APs are managed by a Rendezvous Point (RP).  
In order to join a hierarchically decomposed multicast group, a node generates the hashed location for the RP and sends a join message to that location. After receiving the value of decomposition index \(d\) from the RP, the node invokes the hash function with \(d\) and its location, to achieve the hashed location of the AP of the cell it belongs to. Consequently, the source builds an overlay tree, the Source-to-AP tree, whose vertices are active APs in a topology graph, and another overlay tree, the AP-to-Member tree is also built from the AP, considering each member as the vertex. When a source needs to transmit data packets, it utilizes the unicast-based forwarding strategy of HRPM to propagate data packets to each AP along the Source-to-AP overlay tree. In each cell, instead of constructing an AP-to-Member overlay tree, HGMR uses the cost over progress optimizing broadcast algorithm of GMR to select the next relay nodes at each hop. By adjusting the value for the decomposition index \(d\), the number of members an AP is responsible for does not increase too much. Hence, the use of GMR within each cell instead of the unicast-based forwarding strategy of HRPM contributes to reduce the number of transmissions. When routing to a hashed location (RP or AP), HGMR uses the face routing of HRPM, while when routing from an AP to a set of group members within a cell, it uses the multicast face routing of HRPM. The data delivery in HGMR is shown in Figure 12.  
The main merits of HGMR can be summarized as follows: (1) The membership management of HGMR is very simple and easy without additional cost due to the geographic hashing algorithm; (2) According to the number of the nodes which play the different roles, the data transmission methods for different hierarchies in HGMR make the routing energy-efficient in a way; (3) HGMR is free of the scalability problem in that only manageable destinations exist in a cell.  
However, there are a few drawbacks in HGMR as follows: (1) The simple network partition into a set of cells may lead to sub-optimal routing paths from the root node to multicast group members;(2) All transmissions are concentrated to APs. APs can be changed to another node by hash function, but it is too limited in a cell, and may bring on unbalanced energy consumption around APs; (3) HGMR makes the routing paths inefficient to some extent, in that data packets are forwarded from the upper APs to the lower APs hierarchically, whether the lower APs are closer to the source than the upper APs or not [80].