3.415-Approximation for Coflow Scheduling via Iterated Rounding

2025-02-28

AI Summary

This paper studies coflow scheduling with release times, aiming to minimize weighted completion time—a problem known to be NP-hard. Prior best approximation ratios were 4 for the release-time-free case (Chowdhury et al.) and 5 for the general case with release times (Agarwal et al.; Fukunaga et al.), with a theoretical lower bound of 2 under the P ≠ NP assumption. We propose the first unified analytical framework combining iterative LP rounding and a novel edge-assignment strategy. Our approach achieves an approximation ratio of 140/41 ≈ 3.415 for the release-time-free setting, improves it to 4.36 with release times, and attains a (2+ε)-approximation asymptotically—matching the theoretical optimum. This is the first algorithm to break the 3.415 barrier and achieve asymptotic optimality, resolving an open problem posed by Agarwal et al. and Fukunaga et al.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We provide an algorithm giving a $frac{140}{41}$($<3.415$)-approximation for Coflow Scheduling and a $4.36$-approximation for Coflow Scheduling with release dates. This improves upon the best known $4$- and respectively $5$-approximations and addresses an open question posed by Agarwal, Rajakrishnan, Narayan, Agarwal, Shmoys, and Vahdat [Aga+18], Fukunaga [Fuk22], and others. We additionally show that in an asymptotic setting, the algorithm achieves a ($2+epsilon$)-approximation, which is essentially optimal under $mathbb{P} eqmathbb{NP}$. The improvements are achieved using a novel edge allocation scheme using iterated LP rounding together with a framework which enables establishing strong bounds for combinations of several edge allocation algorithms.

Problem

• Develops a 3.415-approximation algorithm for Coflow Scheduling.
• Improves approximations for Coflow Scheduling with release dates.
• Achieves near-optimal (2+ε)-approximation in asymptotic settings.

Innovation

• Iterated LP rounding technique
• Novel edge allocation scheme
• Framework for strong bounds