Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1612.00989

Online Page Migration on Ring Networks in Uniform Model

Amanj Khorramian·Akira Matsubayashi
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper explores the problem of page migration in ring networks. A ring network is a connected graph, in which each node is connected with exactly two other nodes. In this problem, one of the nodes in a given network holds a page of size D. This node is called the server and the page is a non-duplicable data in the network. Requests are issued by nodes to access the page one after another. Every time a new request is issued, the server must serve the request and may migrate to another node before the next request arrives. A service costs the distance between the server and the requesting node, and the migration costs the distance of the migration multiplied by D. The problem is to minimize the total costs of services and migrations. We study this problem in uniform model, for which the page has a unit size, i.e. D=1. A 3.326-competitive algorithm improving the current best upper bound is designed. We show that this ratio is tight for our algorithm.

Explore related subjects

cs.DScs.DCcs.ITmath.IT

Keep this discovery

BibTeXRIS

Amanj Khorramian, Akira Matsubayashi. 2016-12-03. Online Page Migration on Ring Networks in Uniform Model. https://arxiv.org/abs/1612.00989

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↗