View source for Search problem (linear)

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An optimality problem first formulated by R. Bellman [[#References|[a1]]]. Suppose a particle is located on the real line, its unknown position being characterized by a symmetric probability distribution $F$. A searcher starts at the origin and can move in either direction with constant velocity until the target is found. The problem is to determine a path which minimizes the expected searching time.

W. Franck [[#References|[a2]]] showed that there exist paths with finite expected searching time if and only if $\int|x|\,dF(x)<\infty$. Sufficient conditions for the existence of an optimal search path were established by A. Beck (in [[#References|[a3]]] and subsequent papers in Israel J. Math.). Optimal search paths were constructed [[#References|[a4]]] for the distributions of Gauss, Laplace and Student. A recent survey of the linear search problem, including generalizations and open questions, can be found in [[#References|[a5]]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  R. Bellman,   "Research problem No. 63–9"  ''SIAM Review'' , '''5'''  (1963)  pp. 274</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Franck,   "An optimal search problem"  ''SIAM Review'' , '''7'''  (1965)  pp. 503–512</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  A. Beck,   "On the linear search problem"  ''Israel J. Math.'' , '''2'''  (1964)  pp. 221–228</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  P.J. Rousseeuw,   "Optimal search paths for random variables"  ''J. Comput. Appl. Math.'' , '''9'''  (1983)  pp. 279–286</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top">  F.T. Bruss,   J.B. Robertson,   "A survey of the linear search problem"  ''Math. Scientist'' , '''13'''  (1988)  pp. 75–89</TD></TR></table>