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What and Who
Title:Optimal Sorting with Persistent Comparison Errors
Speaker:Stefano Leucci
coming from:Max-Planck-Institut für Informatik - D1
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, MMCI
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Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 22 January 2019
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
We consider the problem of sorting n elements in the case of persistent comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability p, and comparisons cannot be repeated (Braverman and Mossel, SODA'08).

Sorting perfectly in this model is impossible, and the objective is to minimize the dislocation of each element in the output sequence, that is, the difference between its true rank and its position. Existing lower bounds for this problem show that no algorithm can guarantee, with high probability, maximum dislocation and total dislocation better than Omega(log n) and Omega(n), respectively, regardless of its running time.
We present the first O(n log n)-time sorting algorithm that guarantees both O(log n) maximum dislocation and O(n) total dislocation with high probability.
This settles the time complexity of this problem and shows that comparison errors do not make the problem computationally more difficult: a sequence with the best possible dislocation can be obtained in O(n log n) time and, even without comparison errors, Omega(n log n) time is necessary to guarantee such dislocation bounds.

Contact
Name(s):Nitin Saurabh
Video Broadcast
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Created:
Nitin Saurabh, 01/14/2019 08:43 AM
Last modified:
Uwe Brahm/MPII/DE, 01/22/2019 07:01 AM
  • Nitin Saurabh, 01/14/2019 08:43 AM -- Created document.