## 1 Introduction  
Wireless sensor and actor networks (WSANs) [1; 2; 3] are composed of a large number of sensor nodes and several mobile actors. The mobile actors move in a large area to execute missions, such as rescuing survivors or fire surveillance. The sensor nodes monitor the area and provide supports for the actors. When an event of interest is detected, the sensor node should forward an event report to inform the actor. For the mobility of the actor, its location information is always unavailable for the sensor node, which makes the event report transmission a challenging issue. Location service and search strategy are two popular solutions to solve this problem [4]. In the location service, the actor periodically updates its location information to a subset of sensor nodes and the source can query these selected nodes to obtain the location of the actor. On the other hand, the search strategy is generally developed based on flooding which can forward the packets without the location of targets [5; 6; 7]. Compared with the location service, the search strategy has no overhead when there is no event occurs. Therefore, the search strategy is a reasonable solution for event report transmission to mobile actors. Expanding ring search (ERS) is a predominant search strategy [5]. In ERS, the search packets are broadcast and propagated in the network with a preset time-to-live (TTL) value. The TTL value decreases at every time the packet is relayed. When TTL value expires, the propagation stops. This process is called a _search attempt_. If the target locates within this area, it will reply an acknowledgement (ACK) packet back to the source. Otherwise, the source will eventually time out and initiate another search attempt that covers a larger network area. The setting of TTL reduces the energy consumption compared with simply flooding the search packets all over the network. However, an unsuccessful search attempt results in repetitive broadcasting which increases both search delay and energy consumption. In this paper, we focus on the search strategy design based on ERS. We propose a trail-based search (TS) strategy which takes advantage of actor mobility to improve search efficiency. The basic idea of TS is that: when the actor moves in the area, it leaves its _footprints_ by broadcasting a tiny beacon packet. The footprints are recorded by nearby sensor nodes, and the footprints form a continuous _trail_ in the sensor network. In this case, the search attempt is successful when either the actor or its footprints are discovered. When a footprint is discovered, the search packet will be forwarded along the trail until it is received by the actor. As shown in Figure 1, the trail is much easier to be found than the actor itself, thus the trail-based search may greatly reduce the search delay and energy consumption. Specifically, this paper has the following contributions:  
1. A distributed mechanism is proposed to generate the actor's trail. The footprint information is recorded locally in each sensor node, and it is not required to be forwarded by sensor nodes. Therefore, the overhead is extremely low. Moreover, we formally derive the condition to keep the connectivity of the trail which is important to guarantee reliable event report transmission. 2. We propose the trail-based search (TS) strategy which uses the trail information to improve search efficiency. TS strategy is composed of two phases: the search phase and the chase phase. The search phase is similar to ERS strategy, except that the search attempt is successful when either the actor or its footprints are discovered. In the chase phase, the packets are forwarded along the trail to chase the actor. Moreover, the _effective footprint_ is proposed to balance the efficiency between the search phase and the chase phase. 3. The transmission redundancy generated by the trail is evaluated in this paper. Since the footprints are generated by the broadcast from the actor, multiple sensor nodes can receive the same footprints simultaneously.