Sequences of radius K: How to fetch many huge objects into small memory for pairwise computations

Jerzy W. Jaromczyk, Zbigniew Lonc

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 languageEnglish
Pages (from-to)594-605
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - 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


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