Almost optimal explicit selectors

Research output: Contribution to journalConference article

16 Scopus citations

Abstract

We understand selection by intersection as distinguishing a single element of a set by the uniqueness of its occurrence in some other set. More precisely, given two sets A and B, if A ∩ B = {z}, then element z ∈ A is selected by set B. Selectors are such families S of sets B of some domain that allow to select many elements from sufficiently small subsets A of the domain. Selectors are used in communication protocols for the multiple-access channel, in implementations of distributed-computing primitives in radio networks, and in algorithms for group testing. We give new explicit (n, k, r)-selectors of size script O sign(min [n, k2/k-r+1 polylog n]), for any parameters r ≤ k ≤ n. We establish a lower bound Ω(min [n, k2/k-r+1 · log(n/k)/log(k/(k-r+1))]) on the length of (n, k, r)-selectors, which demonstrates that our construction is within a polylog n factor close to optimal. The new selectors are applied to develop explicit implementations of selection resolution on the multiple-access channel, gossiping in radio networks and an algorithm for group testing with inhibitors.

Original languageEnglish (US)
Pages (from-to)270-280
Number of pages11
JournalLecture Notes in Computer Science
Volume3623
DOIs
StatePublished - Jan 1 2005
Externally publishedYes
Event15th International Symposium on Fundamentals of Computation Theory, FCT 2005 - Lubeck, Germany
Duration: Aug 17 2005Aug 20 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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