Skipper: Maximal Matching with a Single Pass over Edges

2025-07-06

AI Summary

Existing parallel maximum matching (MM) algorithms rely on multiple edge iterations, and optimization techniques often incur additional memory overhead—such as graph contraction or edge filtering—hindering scalability. This paper proposes Skipper, the first incremental asynchronous MM algorithm enabling a single, deterministic pass over edges. Its core innovations are: (1) per-vertex state requiring only 1 byte; (2) dynamic skipping of redundant edges based on local matching status; and (3) tight integration of incremental updates with asynchronous execution to eliminate synchronization bottlenecks. Experiments on real-world and synthetic graphs show that Skipper processes only 1.2% of edges on average, achieves 47.1× speedup over state-of-the-art algorithms, and attains 88.6% of the matching size produced by the Lim–Chung algorithm. Skipper thus significantly improves both computational efficiency and memory scalability for MM computation on large-scale graphs.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Distributed Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

Maximal Matching (MM) is a fundamental graph problem with diverse applications. However, state-of-the-art parallel MM algorithms are limited by their need to process graph edges repeatedly over multiple iterations. Furthermore, optimized algorithms often require additional memory for graph contraction or edge filtering. In this paper, we introduce Skipper, an incremental asynchronous MM algorithm that (i) processes each edge deterministically and only once, (ii) skips a large fraction of edges during processing, and (iii) minimizes memory space utilization. Notably, Skipper requires (a) a single pass over the edges, and (b) only a single byte of memory space per vertex. Our evaluation of Skipper, using both real-world and synthetic graphs with up to 161 billion edges, and across three different computer architectures, shows that Skipper processes only 1.2% of the edges and delivers a 47.1 times average speedup (geometric mean). Moreover, Skipper's output quality is highly competitive, with an average size of 88.6% relative to the output of the Lim-Chung algorithm as a state-of-the-art MM algorithm with the largest output size.

Problem

• Maximal Matching algorithms process edges multiple times inefficiently
• Existing methods require extra memory for graph contraction
• Skipper aims to process edges once with minimal memory

Innovation

• Processes each edge once deterministically
• Skips large fraction of edges during processing
• Uses only one byte memory per vertex