## 1 Introduction  
The existence of end-to-end connectivity becomes infeasible in opportunistic ad hoc networks (OppNets) [1], where message forwarding services suffer from frequent disruption, sparse connectivity, and limited device capability. Unlike vehicular ad hoc networks (VANETs) [2; 3] that broadcast data in confined and dense areas, OppNets are characterized by lower node density, intermittent connectivity, and infrastructure-less connectivity among mobile devices. Alternatively, the research in OppNets often employs the \"store carry-and-forward\" message delivery model: nodes can store messages in local buffers and carry them during movement, until any appropriate forwarding opportunities come out. Because OppNets cannot maintain up-to-date network topology information against frequent link disconnections, geographic routing techniques are employed to convey the message distribution in OppNets. Functionally, geographic routing is based on the location information of mobile devices to relay messages. It allows messages to approach and eventually reach a target node without relying on topology information [4; 5; 6; 7]. Due to the unpredictable nature of contacts between mobile nodes in OppNets, a majority of geographic routing policies replicate a message multiple times to increase the possibility that a target node receives that message. Generally, message replication is performed by either finding better candidate nodes capable of delivering messages to a target node or spraying a limited number of copies of a message in a network. The former policiesuse utility metrics to evaluate the nodal delivery potential, control replication, and find better candidate nodes to increase message delivery [6; 8; 9]. The latter policies assume that a sufficient number of nodes in a network move at higher speeds and in a large coverage area, encounter more nodes, and expedite message delivery to a target node [4; 5]. Despite many efforts in selecting the best candidate node, the concerns of spreading messages toward the direction of a destination node as accurately as possible and the destination's movement are still not well addressed yet for efficient message delivery in OppNets. When OppNets are characterized by the presence of a low node density, it is challenging to deal with the local maximum: a message carrier continues to carry its message in the absence of a better candidate node. Previous studies employed utility-based [9; 10; 11; 12; 13] policies to exploit contact properties, such as contact duration, contact frequency, shorter residual contact time with a target node, etc., to find better candidate nodes. Utility calculated by these policies is commonly referred to as delivery probability (DP) or centrality/temporal closeness with respect to any particular destination. For example, [PERSON] et al. [9] used the duration and frequency of contacts between node pairs to deduce their respective temporal closeness. A node with a higher temporal centrality, calculated by taking all nodes into account or a higher future temporal closeness with a destination, was selected as the next candidate node. [PERSON] et al. [12] proposed a social energy-based routing (SEBAR) protocol based on the concept of a social energy metric. A node with multiple encounters can have higher social energy and be considered a better candidate node. Though these policies can obtain accurate DP or centrality/temporal closeness, they cannot predict if selected nodes are moving toward destinations. This is because the DP or centrality/temporal closeness estimate cannot timely reflect the movement behavior among neighbor nodes in geographic proximity. Additionally, in the absence of a better candidate node, the local maximum remains unresolved. Exploiting the movement information of mobile nodes using geographic information can be beneficial in spraying a limited number of copies of a message toward a direction where a destination likely stays.