Range Majorities and Minorities in Arrays

نویسندگان

چکیده

The problem of parameterized range majority asks us to preprocess a string length n such that, given the endpoints range, one can quickly find all distinct elements whose relative frequencies in that are more than threshold \(\tau\). This is tractable version classical finding mode, which unlikely be solvable polylogarithmic time and linear space. In this paper we give first linear-space solution with optimal \(\mathcal {O}\!\left( {1 / \tau } \right)\) query time, even when \(\tau\) specified query. We then consider data structures space bounded by entropy distribution symbols sequence. For case alphabet size \(\sigma\) polynomial on computer word size, retain within optimally compressed (i.e., sublinear redundancy). Otherwise, either increased an arbitrarily small constant factor or rises any function \((1/\tau )\cdot \omega (1)\). obtain same results complementary minority.

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Range Majorities and Minorities in Arrays

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ژورنال

عنوان ژورنال: Algorithmica

سال: 2021

ISSN: ['1432-0541', '0178-4617']

DOI: https://doi.org/10.1007/s00453-021-00799-7