## 1 Introduction  
Recent years there have been a lot of applications in Wireless Sensor Networks (WSNs), ranging from monitoring to event detection and target tracking. For all these applications, data gathering is one of the primary operations carried out in WSNs [1; 2; 3; 4]. Traditionally, the network is assumed to be dense so that there are end-to-end multi-hop paths within the network, along which the generated data could be routed to the base station. This assumption, however, does not always hold in the scenarios of real network deployments. For example, as the WSN is often deployed in harsh environments, the signal is susceptible to external interference and leads to disconnected and portioned network; and if the network is sparse or the nodes are mobile, the paths to the sink might not always be available. So recently there is a research trend that adopts mobile elements for the message transmission and data gathering in mobile sensor networks [5; 6]. In these schemes mobile data collectors, e.g., autonomous robots, are used to move within the sensing field, collects data from sensor nodes and brings them to the sink. The ordinary nodes, on the other hand, just stay stationary and wait for the mobile data collector to come and pick up the data. So the _funwelling effect_[7], where the energy of nodes near the sink is depleted quickly because of forwarding more data packets than nodes distant from the sink, could be avoided. Mobile elements also make data gathering in a sparse or disconnected network possible because the collector can travel and directly collect the data from sensors. One strategy of data gathering with mobile elements is to map the data gathering problem into the optimization of trajectories of the mobile collector, and various scheduling schemes are proposed to increase the network lifetime or to minimize the traveling distance of mobile elements [1; 3; 4; 6; 8; 9; 10]. In these schemes, however, ordinary nodes should be stationary and there should be paths or tracks available among the nodes, which are not always true in network deployments. Another strategy [11; 12; 13; 14] is to adopt an opportunistic \"Store-Carry-Forward\" routing protocols, the same as those in the Delay-Tolerant Networks [15; 16], for data gathering when both the ordinary nodes and data collector are mobile. Because both the ordinary nodes and the collector are mobile, there is no stable trajectories along which the collector could move within the network for data gathering, neither are the static links between the source node and the collector. So a _flooding_ or _epidemic_ approach is usually adopted for the message routing, which leads to unnecessary transmissions and energy depletion of nodes. In this paper, we study the problem of data gathering in mobile sensor networks with speedy mobile elements, especially when there is no predefined paths or tracks for the data collector. For example, an autonomous underwater vehicle is used as a mobile sink to gather data from a randomly distributed underwater sensor network [17]; in the wildlife monitoring application [11], sensor nodes are attached to the monitoring targets so that they could opportunistically exchange messages and upload the sensed data to the data collector. Yet at these scenarios the \"on-land\" data collector, e.g., SenCar [8], is usually not suitable for the data gathering because the collector moves relatively at low speed, and there might not be any path or track available for the data collector due to the harsh environment of the sensing field. In contrast, a speedy and track-free data collector, e.g., a modeling aircraft actuated by a remote controller or unmanned aerial vehicle, could move to any place within the network as well as to be able to stay stationary at any location. It is ideal to be used as a data collector, and recent events, e.g., Fukushima nuclear reactor explosion, have highlighted the need for unmanned remote sensing in dangerous areas, particularly where structures have collapsed or explosions have occurred [18].