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On Reconstructing a Hidden Permutation

Authors Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, Silvio Lattanzi

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Flavio Chierichetti
Anirban Dasgupta
Ravi Kumar
Silvio Lattanzi

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Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, and Silvio Lattanzi. On Reconstructing a Hidden Permutation. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 604-617, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.604

Abstract

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.

Subject Classification

Keywords
  • Mallows model; Rank aggregation; Reconstruction

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