Non-Adaptive and Adaptive Two-Sided Search with Fast Objects

Koopman introduced in 1946 a two-sided search model. In this search model, the searched object is active and can move one step after each test at most. In this paper we analyze the model of a combinatorial two-sided search by allowing more moves of the searched object after each test. We give search strategies and show that these strategies are optimal. We consider adaptive and non-adaptive strategies. We show the surprising result that with the combinatorial two-sided search on a path graph the optimal non-adaptive search needs the same number of questions as the corresponding adaptive search strategy does. The strategy obtained can also be used to transmit the position of a moving element through a channel. Furthermore, the strategy is a generalization of a group testing strategy to a moving searched element.