eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2014-09-04
604
617
10.4230/LIPIcs.APPROX-RANDOM.2014.604
article
On Reconstructing a Hidden Permutation
Chierichetti, Flavio
Dasgupta, Anirban
Kumar, Ravi
Lattanzi, Silvio
The Mallows model is a classical model for generating noisy perturbations of a hidden permutation, where the magnitude of the
perturbations is determined by a single parameter. In this work we
consider the following reconstruction problem: given several perturbations of a hidden permutation that are generated according
to the Mallows model, each with its own parameter, how to recover
the hidden permutation? When the parameters are approximately known
and satisfy certain conditions, we obtain a simple algorithm for reconstructing the hidden permutation; we also show that these conditions are nearly inevitable for reconstruction. We then provide an algorithm to estimate the parameters themselves. En route we obtain a precise characterization of the swapping probability in the Mallows model.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol028-approx-random2014/LIPIcs.APPROX-RANDOM.2014.604/LIPIcs.APPROX-RANDOM.2014.604.pdf
Mallows model; Rank aggregation; Reconstruction