Constructing k-radius sequences

Details Constructing k-radius sequences Constructing k-radius sequences

2010-06-30

arxiv.org/abs/1006.5812v3

Mathematics

Combinatorics

21 pages, 1 figure. Revision after reviewer comments. Minor changes of phrasing and a few lines of extra explanation added at

Scientific paper

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 < 195 and all k such that k+1 or 2k+1 is prime. For certain k, in particular when 2k+1 is prime, we get a sharper error term using the theory of logarithms.

Affiliated with

Also associated with

No associations

Rating

Constructing k-radius sequences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Constructing k-radius sequences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing k-radius sequences will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-153733