Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1812.05306

Optimal Algorithm for Profiling Dynamic Arrays with Finite Values

Dingcheng Yang·Wenjian Yu·Junhui Deng·Shenghua Liu
View original source ↗Read source document ↗Export metadata ↓

Abstract

How can one quickly answer the most and top popular objects at any time, given a large log stream in a system of billions of users? It is equivalent to find the mode and top-frequent elements in a dynamic array corresponding to the log stream. However, most existing work either restrain the dynamic array within a sliding window, or do not take advantages of only one element can be added or removed in a log stream. Therefore, we propose a profiling algorithm, named S-Profile, which is of $O(1)$ time complexity for every updating of the dynamic array, and optimal in terms of computational complexity. With the profiling results, answering the queries on the statistics of dynamic array becomes trivial and fast. With the experiments of various settings of dynamic arrays, our accurate S-Profile algorithm outperforms the well-known methods, showing at least 2X speedup to the heap based approach and 13X or larger speedup to the balanced tree based approach.

Explore related subjects

cs.DScs.CCcs.SI

Keep this discovery

BibTeXRIS

Dingcheng Yang, Wenjian Yu, Junhui Deng, Shenghua Liu. 2018-12-13. Optimal Algorithm for Profiling Dynamic Arrays with Finite Values. https://arxiv.org/abs/1812.05306

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗