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On the minimality of search paths under absolutely continuous univariate distributions. (English) Zbl 0684.90056

Summary: The linear search problem is concerned with the search for a target located randomly on a line. The target being sought for might be on either side of some starting point. A searcher makes for the target with an upper bound on his speed, using a continuous search path in which he changes his direction many times before reaching his goal. The minimality of average distance (time) from the starting point upon reaching the target is the measure of optimality of search paths. We have obtained sufficient conditions that guarantee the minimality of such search paths whenever the target has an absolutely continuous distribution.

MSC:

90B40 Search theory
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[1] Ahlswede R, Wegener I (1979) Suchprobleme. B. G. Teubner, Stuttgart
[2] Ahlswede R, Wegener I (1987) Search problems. Wiley ? Interscience Series in Discrete Mathematics and Optimization
[3] Balkhi Z (1983) The optimal search problem theory and computations. PhD Thesis, Free (Vrije) University of Brussels
[4] Balkhi Z (1987) The generalized linear search problem, existence of optimal search path. Journal of Operations Research Society of Japan 30:399-421 · Zbl 0642.90061
[5] Balkhi Z (1989) Generalized optimal search paths for continuous univariate random variables. RAIRO ? Operations Research 23:67-96 · Zbl 0667.90052
[6] Beck A (1964) On the linear search problem. Isr J Math 2:221-228 · Zbl 0168.39502 · doi:10.1007/BF02759737
[7] Beck A (1965) More on the linear search problem. Isr J Math 3:61-70 · Zbl 0168.39503 · doi:10.1007/BF02760028
[8] Beck A, Beck M (1984) Son of the linear search problem. Isr J Math 48:109-122 · Zbl 0561.90052 · doi:10.1007/BF02761156
[9] Beck A, Beck M (1986) The linear search problems rides again. Isr J Math 53:365-372 · Zbl 0606.60044 · doi:10.1007/BF02786568
[10] Beck A, Newman D (1970) Yet more on the linear search problem. Isr J Math 8:419-429 · Zbl 0209.20303 · doi:10.1007/BF02798690
[11] Beck A, Warren P (1973) The return of the linear search problem. Isr J Math 14:169-183 · Zbl 0259.62073 · doi:10.1007/BF02762672
[12] Bellman R (1963) Problem 63-9, an optimal search. SIAM Review 5:274 · doi:10.1137/1005070
[13] Franck W (1965) An optimal search problem. SIAM Rev 7:503-512 · Zbl 0136.14701 · doi:10.1137/1007106
[14] Fristedt B, Heath D (1974) Searching for a particle on the real line. Adv Appl Prob 6:79-102 · Zbl 0277.90047 · doi:10.2307/1426208
[15] Rousseeuw P (1983) Optimal search paths for random variables. J comput Appl Math 9:279-286 · Zbl 0517.90039 · doi:10.1016/0377-0427(83)90020-1
[16] Stone L (1975) Theory of optimal search. Academic Press, New York · Zbl 0343.90030
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