Abstract
In this paper we initiate a new area of study dealing with the best way to search a possibly unbounded region for an object. The model for our search procedures is that we must pay costs proportional to the distance of the next probe position relative to our current position. This model is meant to give a realistic cost measure for a robot moving in the plane. Also, we examine the effect of decreasing the amount of a priori information given to a class of search problems.
Problems in this class are very simple analogues of non-trivial problems on searching with bounded error, searching an unbounded region, processing digitized images, robot navigation, and optimization.
We show that for some simple search problems, the relative information of knowing the general direction of the goal is much higher than knowing the distance to the goal.
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References
Baeza-Yates, R., Culberson, J. C., and Rawlins, G. J. E.; “Searching in Unbounded Domains,” unpublished manuscript, 1988.
Bellman, R.; “A Minimization Problem,” Bulletin of the American Mathematical Society, 62, 270, 1956.
Bentley, J. L., and Yao, A. C.-C.; “An Almost Optimal Algorithm for Unbounded Searching,” Information Processing Letters, 5, 82–87, 1976.
Chang, S.-K.; “A Triangular Scanning Technique for Locating Boundary Curves,” Computer Graphics and Image Processing, 3, 313–317, 1974.
Faber, V. and Mycielski, J.; “The Shortest Curve that Meets all the Lines that Meet a Convex Body,” American Mathematical Monthly, 93, 796–801, 1986.
Gluss, B.; “An Alternative Solution to the the ‘Lost at Sea’ Problem,” in 16th National Meeting of the Operations Research Society of America, Pasadena, 1959.
Isbell, J. R.; “An Optimal Search Pattern,” Naval Research Logistics Quarterly, 4, 357–359, 1957.
Joris, H.; “Le Chasseur Perdu dans la Forêt,” (in French), Element der Mathematik, 35, 1–14, 1980.
Karp, R. M., Saks, M., and Widgerson, A.; “On a Search Problem Related to Branch-and-Bound Procedures,” 27th Annual Symposium on Foundations of Computer Science, 19–28, 1986.
Melzak, Z. A.; Companion to Concrete Mathematics: Mathematical Techniques and Various Applications, John Wiley and Sons, Inc., 1973.
Oglivy, C. S.; Tomorrow's Math: Unsolved Problems for the Amateur, Oxford University Press, 1962.
Rivest, R. L., Meyer, A. R., Kleitman, D. J., and Winklmann, K.; “Coping with Errors in Binary Search Procedures,” Journal of Computer and System Sciences, 20, 396–404, 1980.
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© 1988 Springer-Verlag Berlin Heidelberg
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Baeza-Yates, R.A., Culberson, J.C., Rawlins, G.J.E. (1988). Searching with uncertainty extended abstract. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_20
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DOI: https://doi.org/10.1007/3-540-19487-8_20
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