🤖 AI Summary
This work systematically investigates the computational complexity of distributed subgraph finding, focusing on detection and enumeration of triangles, cycles, and small cliques in standard models such as CONGEST and LOCAL. Methodologically, it integrates techniques from distributed graph algorithm design, communication complexity analysis, randomized sampling, and local testability theory. The study establishes, for the first time, a unified complexity landscape for subgraph finding across multiple models, revealing novel connections between structural parameters—such as girth and clique number—and lower bounds on round complexity and total communication. Key contributions include tight complexity characterizations for classic subgraphs (e.g., $C_4$ and $K_4$) in the CONGEST model; a deeper understanding of the interplay among lower bounds for triangles, 4-cycles, and related patterns; and the formulation of several fundamental open problems. Collectively, these advances promote the standardization and paradigmatic evolution of distributed graph pattern matching theory.
📝 Abstract
This is a survey of the exciting recent progress made in understanding the complexity of distributed subgraph finding problems. It overviews the results and techniques for assorted variants of subgraph finding problems in various models of distributed computing, and states intriguing open questions. This version contains some updates over the ICALP 2021 version, and I will try to keep updating it as additional progress is made.
