Alternating search at two locations

In this paper we introduce a new class of search problem which we call 'alt ernating search'. Two searchers starting at given points in different searc h regions, who can move alternately with speed one, or (as a limiting case) simultaneously with combined speed one, seek to find (reach) an object in least expected time. The hidden object is stationary and its location is gi ven by a known distribution over the union of the two search regions. An im portant special case is the 'Double Linear Search Problem' in which both se arch regions are infinite lines, and which has been shown to be equivalent to the 'Asymmetric Rendezvous Search Problem on the Line' (ARSPL). The gene ral results proved here are applied in a concurrent paper of Alpern and Bec k to prove that the strategy conjectured by Baston and Gal to be optimal fo r the convex ARSPL is indeed optimal. Our general results are concerned wit h determining the method of interleaving two given distributions so as to m inimize the first moment of the resulting distribution.