## 1 Introduction
Some geographic-based routing policies considered the movement range of a destination, the location and speed of a node, and the distance for selecting a candidate node to replicate a message with a limited number of copies in a network [4; 5; 8; 14]. In a study by [PERSON] et al. [14], the historical geographic information, including locations and moving speeds, was used to estimate a movement range of a destination, and messages were replicated by two-phase routing policies. [PERSON] et al. [5] considered both homogeneous and heterogeneous scenarios with identical mobility patterns and mobility in restricted areas. Nodal moving speed, distance, and direction were considered in the homogeneous case. In the heterogeneous case, visiting preferences were also used in replicating a message with a limited number of copies. In the literature, most of the geographic routing policies have considered stationary target nodes and used only one-hop nodal information when selecting a candidate node despite using historical information for the movement range of the destination. However, some studies suggested that exploring two-hop neighborhood information can facilitate a good performance in a network where nodes move randomly [6; 15; 16]. Moreover, nodes moving closer to the destination do not indicate that they have frequent contacts with destinations in OppNets. In this paper, we integrate movement information inside a range of one- and two-hop transmission distances and a weighted form of DP estimate for the relay node selection in OppNets. Comprehensively, the location information of the one-hop relay, the destination node's moving direction, and the centrality value of a node are utilized to enhance the performance of a successful delivery ratio and reduce messaging overhead in OppNets. Accordingly, we propose a message-forwarding policy based on movement patterns, named MPMF for brevity, for efficient message distribution in OppNets. Our intention is threefold:  
* All the location information regarding one-hop and two-hop relays and moving directions of two-hop relays with respect to any particular message-carrying node is exploited to select relay nodes moving closer to a destination node. Assuming high node density in the vicinity of a message-carrying node, one- and two-hop nodal information is thus leveraged to improve message forwarding. * A combined weight measure is obtained using the DP values of one-hop and two-hop relays and the moving direction of the two-hop relay. This combined weight is compared with a threshold of weight value to take a message-forwarding decision. * In the absence of two-hop relays, one-hop location information and the moving direction of the target node are exploited. This case is considered when fewer nodes are scattered in some geographic proximity. To resolve this case, the one-hop node's centrality, which measures the node's ability to communicate with other nodes in a network, is used to address the local maximum problem. We conduct an extensive simulation under two synthetic datasets, TVCM [17] and NCCU [18], to examine the efficiency of our proposed policy. The comparative results show that the proposed policy attains a comparable delivery rate with a lower cost than the Epidemic [19], geographic-based spray-and-relay (GSaR) [4], PRoPHETv2 [10], transient community-based (TCB) [20], and temporal closeness and centrality-based (TCCB) [9] policies. Under TVCM, the proposed policy can achieve higher delivery rates of 10, 44, 17, 54, and 45% as compared with the Epidemic, PRoPHETv2, TCCB, TC, and GSaR policies. With a larger scale of the node population under the TVCM mobility model, our policy can achieve a comparable delivery rate at a very low cost. For example, when the number of nodes is 100, the proposed policy can achieve higher delivery rates of 11 and 9% as compared to the TCCB and TC policies and is only 9.5, 6, and 5% lower to those of the Epidemic, PROPHETv2, and GSaR policies.