## 4 Multicast Routing Approaches in DTN
### Social-Aware Multicast Routing in DTN
#### 4.1.1 Contact Probability  
Single-Data Multicast: [PERSON] et al. [34] presented an analytical model to select forwarding nodes with single-data and multiple-data items based on the social network concept, namely node centrality and social community. Forwarding nodes are chosen based on their capabilities, measured by social-based metrics, to forward message bundles to destinations. In Single-Data Multicast (SDM), a minimum number of relays is selected based on Cumulative Contact Probability (CCP), the average probability that a node encounters a random node within a time constraint. Figure 5 shows the SDM data forwarding process. The multicast source S selects K forwarding nodes (i.e., the minimum number of forwarding nodes to guarantee the required delivery ratio within the specified time constraint). Each forwarding node (Rj, i) forwards the message bundle to only encountered nodes (Rj+1, i) with higher centrality metrics than itself and removes its own local copy to ensure that K number of forwarding nodes remain in the network. Multiple-Data Multicast: In Multiple-Data Multicast (MDM) [34], the nodes maintain their destination-awareness about other nodes to select relays from their neighbors. Data will be forwarded to the gateway node if the intended receivers are in other communities. Figure 6 shows the MDM data forwarding process. The multicast source S needs to deliver data items d1 and d2 to destination sets {D1, D2, D3} and {D2, D4}, respectively. S selects R1 to forward data items to D1 and D2 in the same community. R2 is selected by S to forward d1 to D3 in community C. The gateway node G1 in community B acts as the source after receiving the data item from R2. G1 selects forwarding nodes to relay d1 to the next gateway node G2. Finally, G2 acts as the source and selects relays to forward d1 to D3. Overhead is reduced largely with the proposed SDM and MDM mechanism. Figure 5: The SDM data forwarding process [34]. Figure 6: The MDM data forwarding process [34]. Cloud-Based Multicast: [PERSON] et al. [35] presented a cloud-based multicast scheme to address the problem of relay selection for efficient multicasting in MSNs. It is a cost-effective scheme that offers multicasting services in this variant of DTN with a feedback control mechanism. The destination cloud consists of the destinations and the nodes that are frequently in contact with destinations of similar characteristics. The scheme works in the following two phases: Pre-cloud and inside-cloud, as shown in Figure 7. The source makes the forwarding decision based on the forwarding metric when it meets a node during the pre-cloud phase. The forwarding metric is obtained from the feedback control mechanism after capturing the shortest multicast time for a node to forward data to the destinations during the previous multicast process. In the inside-cloud phase, any node that holds the message only forwards the message when it meets the destination. Cloud-based multicasting with a feedback control mechanism disseminates the data rapidly using the local information exchanging scheme only. Although the performance of the cloud-based multicast scheme is unfavorable in the beginning, the feedback mechanism improves the performance and stabilizes after a few rounds. Two-Level Multicast Routing: Two-Level Multicast Routing (TLMR) is a single-copy multicast routing approach that bundles multiple multicast recipients into a single copy of the data packet. [PERSON] et al. [36] intended to reduce transmission costs and achieve an optimal delivery rate and efficient computing resource usage at the same time. This approach switches between one-hop delivery probability and multi-hop delivery probability when selecting the forwarding nodes. In the first level, the message relay selects the relay based on the social-tie strength of the encountered node with multicast destinations. The decision in the second level is made based on the multi-hop delivery probability computed over the most possible route to the destinations.