On search sets of expanding ring search in wireless networks

We focus on the problem of finding the best search set for expanding ring search (ERS) in wireless networks. ERS is widely used to locate randomly selected destinations or information in wireless networks such as wireless sensor networks. In ERS, controlled flooding is employed to search for the destinations in a region limited by a time-to-live (TTL) before the searched region is expanded. The performance of such ERS schemes depends largely on the search set, the set of TTL values that are used sequentially to search for one destination. Using a cost function of searched area size, we identify, through analysis and numerical calculations, the optimum search set for the scenarios where the source is at the center of a circular region and the destination is randomly chosen within the entire network. When the location of the source node and the destination node are both randomly distributed, we provide an almost-optimal search set. This search set guarantees the search cost to be at most 1% higher than the minimum search cost, when the network radius is relatively large.