Bipartite matching under communication constraints

2026-04-12

AI Summary

This work addresses the challenge of achieving efficient centralized scheduling in large-scale data center networks under communication constraints by formulating it as a bipartite matching problem with only local information available. The authors propose a single-round randomized matching algorithm that integrates degree-biased sampling with random sparsification to achieve high-quality matchings using solely local knowledge. Theoretical analysis and experiments demonstrate that degree-biased sampling outperforms existing approaches in sparse scenarios, while deliberately sparsifying connections in dense settings surprisingly increases the number of matched pairs. The algorithm is parameter-free, stable, and highly efficient; packet-level simulations under real traffic traces show it significantly enlarges the network’s stability region, underscoring its practical deployment potential.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements

Abstract

In modern data center networks, thousands of hosts contend for shared link capacity; the scale of these systems makes centralized scheduling impractical. This article models such scheduling as a bipartite matching problem under communication constraints: senders express interest in forming connections, and receivers respond using only locally available information. A class of single-round probabilistic matching algorithms is proposed, built on two key ideas: degree-biased sampling, in which senders use receiver degrees to inform their random selection, and random thinning, in which senders report only a random subset of their connections. Analytical performance guarantees are established for random graph models. In sparse regimes, degree-biased sampling yields a higher expected matching size than prior communication-constrained algorithms; in denser settings, a counterintuitive phenomenon emerges where deliberately restricting available connections through thinning increases the expected number of matches. Combining thinning to degree two with greedy selection produces an algorithm that requires no parameter tuning and, in packet-level simulations with production traffic traces, significantly extends the network stability region. Although motivated by data center network scheduling, the underlying framework of bipartite matching under local information constraints is portable to other resource allocation settings.

Problem

• bipartite matching
• communication constraints
• data center networks
• local information
• resource allocation

Innovation

• degree-biased sampling
• random thinning
• bipartite matching
• communication constraints
• network stability