Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2509.07587

The Expiration Streaming Model: Diameter, $k$-Center, Counting, Sampling, and Friends

Lotte Blank·Sergio Cabello·MohammadTaghi Hajiaghayi·Robert Krauthgamer·Sepideh Mahabadi·André Nusser·Jeff M. Phillips·Jonas Sauer
View original source ↗Read source document ↗Export metadata ↓

Abstract

An important thread in the study of data-stream algorithms focuses on settings where stream items are active only for a limited time. We introduce a new expiration model, where each item arrives with its own arbitrary expiration time. The special case where items expire in the order that they arrive, which we call consistent expirations, contains the classical sliding-window model of Datar, Gionis, Indyk, and Motwani [SICOMP 2002] and its timestamp-based variant of Braverman and Ostrovsky [FOCS 2007]. Our first set of results explores the expiration streaming model and presents algorithms for several fundamental problems, including approximate counting, uniform sampling, and weighted sampling by efficiently tracking active items without explicitly storing them all. Naturally, these algorithms have many immediate applications, e.g., to range counting. Our second and main set of results for the expiration model designs algorithms for the diameter and k-center problems, where items are points in a metric space. Our results significantly extend those known for the special case of sliding-window streams by Cohen-Addad, Schwiegelshohn, and Sohler [ICALP 2016], and obtain a strictly better approximation factor for the diameter in the important special case of high-dimensional Euclidean metrics. We develop new decomposition and coordination techniques along with a geometric dominance framework to filter out redundant points based on both temporal and spatial proximity.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Lotte Blank, Sergio Cabello, MohammadTaghi Hajiaghayi, Robert Krauthgamer, Sepideh Mahabadi, André Nusser, Jeff M. Phillips, Jonas Sauer. 2025-09-09. The Expiration Streaming Model: Diameter, $k$-Center, Counting, Sampling, and Friends. https://arxiv.org/abs/2509.07587

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↗