eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-02-27
36:1
36:13
10.4230/LIPIcs.STACS.2018.36
article
Optimal Dislocation with Persistent Errors in Subquadratic Time
Geissmann, Barbara
Leucci, Stefano
Liu, Chih-Hung
Penna, Paolo
We study the problem of sorting N elements in presence of persistent errors in comparisons: In this classical model, each comparison between two elements is wrong independently with some probability p, but repeating the same comparison gives always the same result. The best known algorithms for this problem have running time O(N^2) and achieve an optimal maximum dislocation of O(log N) for constant error probability. Note that no algorithm can achieve dislocation o(log N), regardless of its running time.
In this work we present the first subquadratic time algorithm with optimal maximum dislocation: Our algorithm runs in tilde{O}(N^{3/2}) time and guarantees O(log N) maximum dislocation with high probability. Though the first version of our algorithm is randomized, it can be derandomized by extracting the necessary random bits from the results of the comparisons (errors).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol096-stacs2018/LIPIcs.STACS.2018.36/LIPIcs.STACS.2018.36.pdf
sorting
recurrent comparison errors
maximum dislocation