Greedy but Smart: Local Matching for Large-Scale and Semi-Streamed Bipartite Graphs

Paper in proceeding, 2026

The assignment problem, also known as maximum-weight bipartite matching, is a fundamental primitive in applications such as resource allocation and data association. For large-scale graphs that exceed main-memory capacity, however, exact solutions become computationally infeasible. As a practical alternative, we study greedy matching algorithms considering a semi-streaming model with only O(n log n) words of storage for graphs with n nodes. We implement and evaluate several single-pass greedy algorithms with bounded approximation guarantees that exploit structural properties of the input graph, considering streaming variants where edges or partial neighborhoods arrive sequentially. To further improve performance, we introduce cache-efficient chunking and sharding mechanisms that optimize data access during streaming. Experimental results show that our best-performing algorithm computes a matching with a weight 25% greater than Feigenbaum et al.’s classic fourth algorithm on the Netflix prize dataset in a slightly shorter time-frame while using an equivalent amount of memory (550 MB). When verifying on large-scale synthetic graphs, that same algorithm produced near-optimal matchings, that is, within 3.3% of the optimum, while processing a graph with more than 60 million nodes and 500 million edges in under 500 seconds. These results combined advocate that simple local greedy strategies can provide scalable and memory-efficient solutions for large-scale graph matching in streaming environments.