Alpern, Steven and Beck, A. (1999) Asymmetric rendezvous on the line is a double linear search problem. Mathematics of operations research, 24 (3). pp. 604-618. ISSN 0364-765X
We apply a new method of analysis to the asymmetric rendezvous search problem on the line (ARSPL). This problem, previously studied in a paper of Alpern and Gal (1995), asks how two blind, speed one players placed a distance d apart on the line, can find each other in minimum expected time. The distance d is drawn from a known cumulative probability distribution G, and the players are faced in random directions. We show that the ARSPL is strategically equivalent to a new problem we call the double linear search problem (DLSP), where an object is placed equiprobably on one of two lines, and equiprobably at positions ±d. A searcher is placed at the origin of each of these lines. The two searchers move with a combined speed of one, to minimize the expected time before one of them finds the object. Using results from a concurrent paper of the first author and J. V. Howard (1998), we solve the DLSP (and hence the ARSPL) for the case where G is convex on its support, and show that the solution is that conjectured in a paper of Baston and Gal (1998).
|Additional Information:||© 1999 Mathematics of Operations Research|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
|Date Deposited:||13 Feb 2010 12:12|
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