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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Shortest paths through pseudorandom points in the $ d$-cube


Author: J. Michael Steele
Journal: Proc. Amer. Math. Soc. 80 (1980), 130-134
MSC: Primary 65C99; Secondary 60D05
DOI: https://doi.org/10.1090/S0002-9939-1980-0574522-4
MathSciNet review: 574522
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Abstract: A lower bound for the length of the shortest path through n points in $ {[0,1]^d}$ is given in terms of the discrepancy function of the n points. This bound is applied to obtain an analogue for several pseudorandom sequences to the known limit behavior of the length of the shortest path through n independent uniformly distributed random observations from $ {[0,1]^d}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0574522-4
Keywords: Discrepancy, pseudorandom, shortest paths, uniform distribution
Article copyright: © Copyright 1980 American Mathematical Society