Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0802.1685

Generalized Whac-a-Mole

Marcin Bienkowski·Marek Chrobak·Christoph Durr·Mathilde Hurand·Artur Jez·Lukasz Jez·Jakub Lopuszanski·Grzegorz Stachowiak
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider online competitive algorithms for the problem of collecting weighted items from a dynamic set S, when items are added to or deleted from S over time. The objective is to maximize the total weight of collected items. We study the general version, as well as variants with various restrictions, including the following: the uniform case, when all items have the same weight, the decremental sets, when all items are present at the beginning and only deletion operations are allowed, and dynamic queues, where the dynamic set is ordered and only its prefixes can be deleted (with no restriction on insertions). The dynamic queue case is a generalization of bounded-delay packet scheduling (also referred to as buffer management). We present several upper and lower bounds on the competitive ratio for these variants.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Marcin Bienkowski, Marek Chrobak, Christoph Durr, Mathilde Hurand, Artur Jez, Lukasz Jez, Jakub Lopuszanski, Grzegorz Stachowiak. 2008-02-12. Generalized Whac-a-Mole. https://arxiv.org/abs/0802.1685

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↗