Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1407.4498

Online Packet-Routing in Grids with Bounded Buffers

Guy Even·Moti Medina
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present deterministic and randomized algorithms for the problem of online packet routing in grids in the competitive network throughput model \cite{AKOR}. In this model the network has nodes with bounded buffers and bounded link capacities. The goal in this model is to maximize the throughput, i.e., the number of delivered packets. Our deterministic algorithm is the first online algorithm with an $O\left(\log^{O(1)}(n)\right)$ competitive ratio for uni-directional grids (where $n$ denotes the size of the network). The deterministic online algorithm is centralized and handles packets with deadlines. This algorithm is applicable to various ranges of values of buffer sizes and communication link capacities. In particular, it holds for buffer size and communication link capacity in the range $[3 \ldots \log n]$. Our randomized algorithm achieves an expected competitive ratio of $O(\log n)$ for the uni-directional line. This algorithm is applicable to a wide range of buffer sizes and communication link capacities. In particular, it holds also for unit size buffers and unit capacity links. This algorithm improves the best previous $O(\log^2 n)$-competitive ratio of Azar and Zachut \cite{AZ}.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Guy Even, Moti Medina. 2014-07-16. Online Packet-Routing in Grids with Bounded Buffers. https://arxiv.org/abs/1407.4498

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↗