Estimating the distance to a monotone function

Nir Ailon, Bernard Chazelle, Seshadhri Comandur, Ding Liu

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In standard property testing, the task is to distinguish between objects that have a property ℘ and those that are ε-far from ℘, for some ε > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy ℘. This implies that property testing in and of itself cannot be expected to yield any information whatsoever about the distance from the object to the property. We address this problem in this paper, restricting our attention to monotonicity testing. A function f : {1, . . . ,n} → R is at distance εf from being monotone if it can (and must) be modified at εfn places to become monotone. For any fixed δ > 0, we compute, with probability at least 2/3, an interval [(1/2-δ)ε, ε] that encloses εf. The running time of our algorithm is O(εf-1 log log εf-1 log n), which is optimal within a factor of log log εf-1 and represents a substantial improvement over previous work. We give a second algorithm with an expected running time of O(εf-1 log n log log log n).

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsKlaus Jansen, Sanjeev Khanna, Jose D. P. Rolim, Dana Ron
PublisherSpringer Verlag
Pages229-236
Number of pages8
ISBN (Print)3540228942, 9783540228943
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3122
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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