Geodesic
Complexity of self-correcting algorithms for two sorting problems
Diskretnaya Matematika, Tome 1 (1989) no. 3, pp. 111-120

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For a standard sorting problem for an $n$-element set we obtain an algorithm, optimal with respect to order, that corrects up to $k(n)$ incorrect comparisons of elements of a sortable set. We show that this algorithm is asymptotically optimal when $k=o(\log n)$. We also obtain a self-correcting algorithm, optimal with respect to order, for a sorting problem of a set that is isomorphic to a Boolean algebra. 
@article{DM_1989_1_3_a11,
     author = {V. V. Morozenko},
     title = {Complexity of self-correcting algorithms for two sorting problems},
     journal = {Diskretnaya Matematika},
     pages = {111--120},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1989_1_3_a11/}
}
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V. V. Morozenko. Complexity of self-correcting algorithms for two sorting problems. Diskretnaya Matematika, Tome 1 (1989) no. 3, pp. 111-120. http://geodesic.mathdoc.fr/item/DM_1989_1_3_a11/