Sorting and selection with imprecise comparisons

Miklós Ajtai, Vitaly Feldman, Avinatan Hassidim, Jelani Nelson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

21 Scopus citations


In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences amongst n elements of a human subject. The method requires performing all comparisons then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decision-making of the human subject, who acts as an imprecise comparator. We consider a simple model of the imprecise comparisons: there exists some δ>0 such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least δ, then the comparison will be made correctly; when the two elements have values that are within δ, the outcome of the comparison is unpredictable. This δ corresponds to the just noticeable difference unit (JND) or difference threshold in the psychophysics literature, but does not require the statistical assumptions used to define this value. In this model, the standard method of paired comparisons minimizes the errors introduced by the imprecise comparisons at the cost of comparisons. We show that the same optimal guarantees can be achieved using 4 n 3/2 comparisons, and we prove the optimality of our method. We then explore the general tradeoff between the guarantees on the error that can be made and number of comparisons for the problems of sorting, max-finding, and selection. Our results provide close-to-optimal solutions for each of these problems.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2009
Externally publishedYes
Event36th International Colloquium on Automata, Languages and Programming, ICALP 2009 - Rhodes, Greece
Duration: 5 Jul 200912 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5555 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference36th International Colloquium on Automata, Languages and Programming, ICALP 2009


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