  We consider a new type of asymmetric rendezvous search problem in which Agent
II needs to give Agent I a `gift' which can be in the form of information or
material. The gift can either be transfered upon meeting, as in traditional
rendezvous, or it can be dropped o? by II at a location he passes, in the hope
it will be found by I. The gift might be a water bottle for a traveller lost in
the desert; a supply cache for Lieutenant Scott in the Antarctic; or important
information (left as a gift). The common aim of the two agents is to minimize
the time taken for I to either meet II or find the gift. We find optimal agent
paths and droppo? times when the search region is a line, the initial distance
between the players is known and one or both of the players can leave gifts.
When there are no gifts this is the classical asymmetric rendezvous problem
solved by Alpern and Gal in 1995 [10]. We exhibit strategies solving these
various problems and use a `rendezvous algorithm' to establish their
optimality.
