Abstract
Let a1, a2,..., am be a sequence over [n] = {1,... n}. We say that a sequence a1, a2,... a m has the k-radius property if every pair of different elements in [n] occurs at least once within distance at most k; the distance d(a i, aj) = |i-j|. We demonstrate lower and (asymptotically) matching upper bounds for sequences with the k-radius property. Such sequences are applicable, for example, in computations of two-argument functions for all (2n) pairs of large objects such as medical images, bitmaps or matrices, when processing occurs in a memory of size capable of storing k + 1 objects, k < n. We focus on the model when elements are read into the memory in a FIFO fashion that correspond to streaming the data or a special type of caching. We present asymptotically optimal constructions; they are based on the Euler totient theorem and recursion.
Original language | English |
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Pages (from-to) | 594-605 |
Number of pages | 12 |
Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
Volume | 3341 |
DOIs | |
State | Published - 2004 |
Bibliographical note
Funding Information:★★This work was supported in part by the University of Kentucky subcontract of grants 5P20RR016481-03 and 2P20RR016481-04 from NCRR-NIH, and by KY NSF EPSCOR grant EPS-0132295.
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science