eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
29:1
29:13
10.4230/LIPIcs.SoCG.2020.29
article
A Generalization of Self-Improving Algorithms
Cheng, Siu-Wing
1
https://orcid.org/0000-0002-3557-9935
Chiu, Man-Kwun
2
Jin, Kai
1
https://orcid.org/0000-0003-3720-5117
Wong, Man Ting
1
HKUST, Hong Kong, China
Institut für Informatik, Freie Universität Berlin, Germany
Ailon et al. [SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances x₁,⋯,x_n follow some unknown product distribution. That is, x_i comes from a fixed unknown distribution 𝒟_i, and the x_i’s are drawn independently. After spending O(n^{1+ε}) time in a learning phase, the subsequent expected running time is O((n+ H)/ε), where H ∈ {H_S,H_DT}, and H_S and H_DT are the entropies of the distributions of the sorting and DT output, respectively. In this paper, we allow dependence among the x_i’s under the group product distribution. There is a hidden partition of [1,n] into groups; the x_i’s in the k-th group are fixed unknown functions of the same hidden variable u_k; and the u_k’s are drawn from an unknown product distribution. We describe self-improving algorithms for sorting and DT under this model when the functions that map u_k to x_i’s are well-behaved. After an O(poly(n))-time training phase, we achieve O(n + H_S) and O(nα(n) + H_DT) expected running times for sorting and DT, respectively, where α(⋅) is the inverse Ackermann function.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol164-socg2020/LIPIcs.SoCG.2020.29/LIPIcs.SoCG.2020.29.pdf
expected running time
entropy
sorting
Delaunay triangulation