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Inthis paper we introduce a new class of search problem which wecall `alternating search'. Two searchers starting at given pointsin different search regions, who can move alternately with speedone, or (as a limiting case) simultaneously with combined speedone, seek to find (reach) an object in least expected time. Thehidden object is stationary and its location is given by a knowndistribution over the union of the two search regions. An importantspecial case is the `Double Linear Search Problem' in which bothsearch regions are infinite lines, and which has been shown tobe equivalent to the `Asymmetric Rendezvous Search Problem onthe Line' (ARSPL). The general results proved here are appliedin a concurrent paper of Alpern and Beck to prove that the strategyconjectured by Baston and Gal to be optimal for the convex ARSPLis indeed optimal. Our general results are concerned with determiningthe method of interleaving two given distributions so as to minimizethe first moment of the resulting distribution. |
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