Keywords and Synonyms
Searching for a point in a line; Searching in one dimension; Searching for a line (or a plane) of known slope in the plane (or a 3D space)
Problem Definition
The problem is to design a strategy for a searcher (or a number of searchers) located initially at some start point on a line to reach an unknown target point. The target point is detected only when a searcher is located on it. There are several variations depending on the information about the target point, how many parallel searchers are available and how they can communicate, and the type of algorithm. The cost of the search algorithm is defined as the distance traveled until finding the point relative to the distance of the starting point to the target. This entry only covers deterministic algorithms.
Key Results
Consider just one searcher. If one knows the direction to the target, the solution is trivial and the relative cost is 1. If one knows the distance to the target, the solution is also simple....
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Recommended Reading
Alpern, S., Gal, S.: The Theory of Search Games and Rendevouz. Kluwer Academic Publishers, Dordrecht (2003)
Baeza-Yates, R., Culberson, J., Rawlins, G.: Searching in the Plane. Inf. Comput. 106(2), 234–252 (1993) Preliminary version as Searching with uncertainty. In: Karlsson, R., Lingas, A. (eds.) Proceedings SWAT 88, First Scandinavian Workshop on Algorithm Theory. Lecture Notes in Computer Science, vol. 318, pp. 176–189. Halmstad, Sweden (1988)
Baeza-Yates, R., Schott, R.: Parallel searching in the plane. Comput. Geom. Theor. Appl. 5, 143–154 (1995)
Blum, A., Raghavan, P., Schieber, B.: Navigating in Unfamiliar Geometric Terrain. In: On Line Algorithms, pp. 151–155, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, Providence RI (1992) Preliminary Version in STOC 1991, pp. 494–504
Demaine, E., Fekete, S., Gal, S.: Online searching with turn cost. Theor. Comput. Sci. 361, 342–355 (2006)
Gal, S.: Minimax solutions for linear search problems. SIAM J. Appl. Math. 27, 17–30 (1974)
Gal, S.: Search Games, pp. 109–115, 137–151, 189–195. Academic Press, New York (1980)
Hipke, C., Icking, C., Klein, R., Langetepe, E.: How to Find a point on a line within a Fixed distance. Discret. Appl. Math. 93, 67–73 (1999)
Kao, M.-Y., Reif, J.H., Tate, S.R.: Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem. Inf. Comput. 131(1), 63–79 (1996) Preliminary version in SODA '93, pp. 441–447
Lopez-Ortiz, A.: On-Line Target Searching in Bounded and Unbounded Domains: Ph. D. Thesis, Technical Report CS-96-25, Dept. of Computer Sci., Univ. of Waterloo (1996)
Lopez-Ortiz, A., Schuierer, S.: The Ultimate Strategy to Search on m Rays? Theor. Comput. Sci. 261(2), 267–295 (2001)
Papadimitriou, C.H., Yannakakis, M.: Shortest Paths without a Map. Theor. Comput. Sci. 84, 127–150 (1991) Preliminary version in ICALP '89
Schuierer, S.: Lower bounds in on-line geometric searching. Comput. Geom. 18, 37–53 (2001)
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Baeza-Yates, R. (2008). Deterministic Searching on the Line. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_106
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DOI: https://doi.org/10.1007/978-0-387-30162-4_106
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