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We study self-improving sorting with hidden partitions. Our result is an optimal algorithm which runs in expected time O(H(pi(I)) + n), where I is the given input which contains n elements to be sorted, pi(I) is the output which are the ranks of all element in I, and H(pi(I)) denotes the entropy of the output.
Ailon et al. [SICOMP11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances $x_1,cdots,x_n$ follow some unknown emph{product distribution}. That is, $x_i$ comes from a fixed unknown distribution $ma
The construction of an unbounded polyhedron from a jagged convex cap is described, and several of its properties discussed, including its relation to Alexandrovs limit angle.
Taxonomies have been widely used in various machine learning and text mining systems to organize knowledge and facilitate downstream tasks. One critical challenge is that, as data and business scope grow in real applications, existing taxonomies need
Let $T(d,r) = (r-1)(d+1)+1$ be the parameter in Tverbergs theorem, and call a partition $mathcal I$ of ${1,2,ldots,T(d,r)}$ into $r$ parts a Tverberg type. We say that $mathcal I$ occurs in an ordered point sequence $P$ if $P$ contains a subsequence
Nicolas and DeSalvo and Pak proved that the partition function $p(n)$ is log concave for $n geq 25$. Chen, Jia and Wang proved that $p(n)$ satisfies the third order Tur{a}n inequality, and that the associated degree 3 Jensen polynomials are hyperboli