Bipartite matching under communication constraints

TL;DR

This paper introduces probabilistic bipartite matching algorithms for data center scheduling that operate under communication constraints, improving matchings by leveraging local information and randomization.

Contribution

It proposes novel degree-biased sampling and random thinning techniques with analytical guarantees, enhancing matching efficiency in various network density regimes.

Findings

Degree-biased sampling outperforms prior algorithms in sparse regimes.

Thinning can increase matchings in denser settings, contrary to intuition.

The combined algorithm extends network stability in simulations.

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.