Abstract
We consider the problem of searching on m current rays for a target of unknown location. If no upper bound on the distance to the target is known in advance, then the optimal competitive ratio is 1 + 2mm/(m − 1)m−1. We show that if an upper bound of D on the distance to the target is known in advance, then the competitive ratio of any searchst rategy is at least 1 + 2mm/(m − 1)m−1 − O(1/log2D) which is also optimal—but in a stricter sense.
We also construct a search strategy that achieves this ratio. Astonishingly, our strategy works equally well for the unbounded case, that is, if the target is found at distance D from the starting point, then the competitive ratio is 1 + 2mm/(m − 1)m−1 − O(1/log2D) and it is not necessary for our strategy to know an upper bound on D in advance.
This research is supported by the DFG-Project “Diskrete Probleme”, No. Ot 64/8-1.
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López-Ortiz, A., Schuierer, S. (1998). The Ultimate Strategy to Search on m Rays?. In: Hsu, WL., Kao, MY. (eds) Computing and Combinatorics. COCOON 1998. Lecture Notes in Computer Science, vol 1449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68535-9_11
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DOI: https://doi.org/10.1007/3-540-68535-9_11
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