R. Blackburn, Simon and F. McKee, James (2012) Constructing k-radius sequences. Mathematics of Computation, 81 (280).
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An n-ary k-radius sequence is a finite sequence of elements taken from an alphabet of size n such that any two distinct elements of the alphabet occur within distance k of each other somewhere in the sequence. These sequences were introduced by Jaromczyk and Lonc to model a caching strategy for computing certain functions on large data sets such as medical images. Let f_k(n) be the shortest length of any k-radius sequence. We improve on earlier estimates for f_k(n) by using tilings and logarithms. The main result is that f_k(n) ~ n^2/(2k) as n tends to infinity whenever a certain tiling of Z^r exists. In particular this result holds for infinitely many k, including all k
This is a Approved version This version's date is: 10/2012 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/9fea9fb2-8a44-7c30-4131-c45e9ac88134/6/
Deposited by Research Information System (atira) on 15-Jul-2013 in Royal Holloway Research Online.Last modified on 15-Jul-2013
21 pages, 1 figure. Improved error term in the main theorem for infinitely many k. Revised Open Problems, with some heuristic discussion