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- W4301414980 abstract "Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative frequencies in that range are more than a threshold $tau$. Subsequent authors have reduced their time and space bounds such that, when $tau$ is given at preprocessing time, we need either $Oh{n log (1 / tau)}$ space and optimal $Oh{1 / tau}$ query time or linear space and $Oh{(1 / tau) log log sigma}$ query time, where $sigma$ is the alphabet size. In this paper we give the first linear-space solution with optimal $Oh{1 / tau}$ query time. For the case when $tau$ is given at query time, we significantly improve previous bounds, achieving either $Oh{n log log sigma}$ space and optimal $Oh{1 / tau}$ query time or compressed space and $Oh{(1 / tau) log frac{log (1 / tau)}{log w}}$ query time. Along the way, we consider the complementary problem of parameterized range minority that was recently introduced by Chan et al. (2012), who achieved linear space and $Oh{1 / tau}$ query time even for variable $tau$. We improve their solution to use either nearly optimally compressed space with no slowdown, or optimally compressed space with nearly no slowdown. Some of our intermediate results, such as density-sensitive query time for one-dimensional range counting, may be of independent interest." @default.
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- W4301414980 date "2012-10-05" @default.
- W4301414980 modified "2023-09-29" @default.
- W4301414980 title "Better Space Bounds for Parameterized Range Majority and Minority" @default.
- W4301414980 doi "https://doi.org/10.48550/arxiv.1210.1765" @default.
- W4301414980 hasPublicationYear "2012" @default.
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