Improved Bounds for Scheduling Flows under Endpoint Capacity Constraints

Searidang Pa; Rajmohan Rajaraman; David Stalfa

Home/Archive/arXiv

arXiv · 2111.08148

Improved Bounds for Scheduling Flows under Endpoint Capacity Constraints

Searidang Pa·Rajmohan Rajaraman·David Stalfa

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study flow scheduling under node capacity constraints. We are given capacitated nodes and an online sequence of jobs, each with a release time and a demand to be routed between two nodes. A schedule specifies which jobs are routed in each step, guaranteeing that the total demand on a node in any step is at most its capacity. A key metric in this scenario is response time: the time between a job's release and its completion. Prior work shows no un-augmented algorithm is competitive for average response time, and that a constant factor competitive ratio is achievable with augmentation exceeding 2 (Dinitz-Moseley Infocom 2020). For maximum response time, the best known result is a 2-competitive algorithm with a augmentation 4 (Jahanjou et al SPAA 2020). We improve these bounds under various response time objectives. We show that, without resource augmentation, the best competitive ratio for maximum response time is $\Omega(n)$, where $n$ is the number of nodes. Our Proportional Allocation algorithm uses $(1+\varepsilon)$ resource augmentation to achieve a $(1/\varepsilon)$-competitive ratio in the setting with general demands and capacities, and splittable jobs. Our Batch Decomposition algorithm is $2$-competitive (resp., optimal) for maximum response time using resource augmentation 2 (resp., 4) in the setting with unit demands and capacities, and unsplittable jobs. We also derive bounds for the simultaneous approximation of average and maximum response time metrics.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Searidang Pa, Rajmohan Rajaraman, David Stalfa. 2021-11-16. Improved Bounds for Scheduling Flows under Endpoint Capacity Constraints. https://arxiv.org/abs/2111.08148

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

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

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↗