Minimization of Weighted Completion Times in Path-based Coflow Scheduling

Alexander Eckl; Luisa Peter; Maximilian Schiffer; Susanne Albers

Home/Archive/arXiv

arXiv · 1911.13085

Minimization of Weighted Completion Times in Path-based Coflow Scheduling

Alexander Eckl·Luisa Peter·Maximilian Schiffer·Susanne Albers

View original source ↗Read source document ↗Export metadata ↓

Abstract

Coflow scheduling models communication requests in parallel computing frameworks where multiple data flows between shared resources need to be completed before computation can continue. In this paper, we introduce Path-based Coflow Scheduling, a generalized problem variant that considers coflows as collections of flows along fixed paths on general network topologies with node capacity restrictions. For this problem, we minimize the coflows' total weighted completion time. We show that flows on paths in the original network can be interpreted as hyperedges in a hypergraph and transform the path-based scheduling problem into an edge scheduling problem on this hypergraph. We present a $(2\lambda + 1)$-approximation algorithm when node capacities are set to one, where $\lambda$ is the maximum number of nodes in a path. For the special case of simultaneous release times for all flows, our result improves to a $(2\lambda)$-approximation. Furthermore, we generalize the result to arbitrary node constraints and obtain a $(2\lambda\Delta + 1)$- and a $(2\lambda\Delta)$-approximation in the case of general and zero release times, where $\Delta$ captures the capacity disparity between nodes.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Alexander Eckl, Luisa Peter, Maximilian Schiffer, Susanne Albers. 2019-11-29. Minimization of Weighted Completion Times in Path-based Coflow Scheduling. https://arxiv.org/abs/1911.13085

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↗