Tolerant property testing and distance approximation

Michal Parnas*, Dana Ron, Ronitt Rubinfeld

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we study a generalization of standard property testing where the algorithms are required to be more tolerant with respect to objects that do not have, but are close to having, the property. Specifically, a tolerant property testing algorithm is required to accept objects that are ε{lunate}1-close to having a given property P and reject objects that are ε{lunate}2-far from having P, for some parameters 0 ≤ ε{lunate}1 < ε{lunate}2 ≤ 1. Another related natural extension of standard property testing that we study, is distance approximation. Here the algorithm should output an estimate over(ε{lunate}, ̂) of the distance of the object to P, where this estimate is sufficiently close to the true distance of the object to P. We first formalize the notions of tolerant property testing and distance approximation and discuss the relationship between the two tasks, as well as their relationship to standard property testing. We then apply these new notions to the study of two problems: tolerant testing of clustering and distance approximation for monotonicity. We present and analyze algorithms whose query complexity is either polylogarithmic or independent of the size of the input.

Original languageEnglish
Pages (from-to)1012-1042
Number of pages31
JournalJournal of Computer and System Sciences
Issue number6
StatePublished - Sep 2006


  • Approximation
  • Clustering
  • Property testing
  • Sublinear algorithms


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