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Intelligent systems. Theory and applications, 2017, Volume 21, Issue 3, Pages 41–64
(Mi ista10)
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This article is cited in 1 scientific paper (total in 1 paper)
Algorithms of moving of the end of chain to the given point
I. O. Berger Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
The problem of chains is investigated.
Results on the existence of chains obtained from given chain by moving of the end of the chain to a given point; Bounds of the minimum of the Euclidean distance between chains obtained from each other by moving of the end to a given point; possible number of chains obtained by moving the end to a given point and differing by the minimum number of elements from a given chain; the possible number of chains that are at the minimum distance from the given and obtained by moving the end of the chain to a given point, for $ n = 2 $ and $ n = 3 $.
Algorithms for moving the end of a chain to a given point are described: an exponential algorithm that sorts out all possible chains with step $\varepsilon$, a linear algorithm giving an approximate solution for Euclidean distance, and a linear algorithm giving an exact answer for the Hamming distance and approximate for the Euclidean distance.
Keywords:
chain, algorithm, upper bounds, lower bounds, Euclidean distance, Hamming distance.
Citation:
I. O. Berger, “Algorithms of moving of the end of chain to the given point”, Intelligent systems. Theory and applications, 21:3 (2017), 41–64
Linking options:
https://www.mathnet.ru/eng/ista10 https://www.mathnet.ru/eng/ista/v21/i3/p41
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