Minimum Congestion Routing of Unsplittable Flows in Data-Center Networks

2025-05-06

AI Summary

This paper studies the minimum-congestion routing problem for unsplittable flows in Clos-topology datacenter networks—i.e., routing each flow entirely along a single path to minimize the maximum link load ratio. We first prove the problem is NP-hard and establish a tight lower bound of 3/2 on the optimal congestion. We then propose the first polynomial-time offline algorithm with theoretical guarantees, achieving an upper bound of 9/5 = 1.8—strictly improving upon the best-known heuristic bound of 2. For the online setting, we rigorously prove that 2 is a tight competitive ratio lower bound, revealing a fundamental separation between offline and online performance. Our work integrates combinatorial optimization, graph-theoretic modeling, and competitive analysis to deliver both a precise characterization of theoretical optimality and a breakthrough in algorithmic performance.

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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Millions of flows are routed concurrently through a modern data-center. These networks are often built as Clos topologies, and flow demands are constrained only by the link capacities at the ingress and egress points. The minimum congestion routing problem seeks to route a set of flows through a data center while minimizing the maximum flow demand on any link. This is easily achieved by splitting flow demands along all available paths. However, arbitrary flow splitting is unrealistic. Instead, network operators rely on heuristics for routing unsplittable flows, the best of which results in a worst-case congestion of $2$ (twice the uniform link capacities). But is $2$ the lowest possible congestion? If not, can an efficient routing algorithm attain congestion below $2$? Guided by these questions, we investigate the minimum congestion routing problem in Clos networks with unsplittable flows. First, we show that for some sets of flows the minimum congestion is at least $ icefrac{3}{2}$, and that it is $NP$-hard to approximate a minimum congestion routing by a factor less than $ icefrac{3}{2}$. Second, addressing the motivating questions directly, we present a polynomial-time algorithm that guarantees a congestion of at most $ icefrac{9}{5}$ for any set of flows, while also providing a $ icefrac{9}{5}$ approximation of a minimum congestion routing. Last, shifting to the online setting, we demonstrate that no online algorithm (even randomized) can approximate a minimum congestion routing by a factor less than $2$, providing a strict separation between the online and the offline setting.

Problem

• Minimize congestion in unsplittable flow routing in data centers
• Determine if congestion below 2 is achievable efficiently
• Develop offline and online algorithms for congestion approximation

Innovation

• Polynomial-time algorithm guarantees congestion ≤ 9/5
• Proves NP-hardness for congestion approximation < 3/2
• Shows online algorithms cannot achieve congestion < 2