Distributed Butterfly Analysis using Mobile Agents

2025-06-21

AI Summary

This paper addresses the distributed butterfly (4-cycle) counting problem in bipartite graphs, aiming to efficiently identify cohesive substructures. Existing approaches rely on global topological knowledge and incur high communication overhead. To overcome these limitations, we propose the first mobile-agent-based algorithm that requires no global information: it achieves fully decentralized collaborative counting via local encounter mechanisms, self-organized spanning tree construction, and lightweight leader election. A key innovation is a dynamic pairwise encounter strategy among adjacent agents—requiring only locally ordered node IDs—naturally supporting dynamic networks and general graph extensions. Our algorithm computes node-level butterfly counts in O(Δ) rounds, with total time complexity O(Δ + min{|A|, |B|}), communication rounds O(n log λ), and per-node memory usage O(log λ) bits—significantly improving upon state-of-the-art distributed solutions.

Technology Category

• Search and Optimization: Distributed Search
• Multiagent Systems: Distributed Problem Solving
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Butterflies, or 4-cycles in bipartite graphs, are crucial for identifying cohesive structures and dense subgraphs. While agent-based data mining is gaining prominence, its application to bipartite networks remains relatively unexplored. We propose distributed, agent-based algorithms for emph{Butterfly Counting} in a bipartite graph $G((A,B),E)$. Agents first determine their respective partitions and collaboratively construct a spanning tree, electing a leader within $O(n log λ)$ rounds using only $O(log λ)$ bits per agent. A novel meeting mechanism between adjacent agents improves efficiency and eliminates the need for prior knowledge of the graph, requiring only the highest agent ID $λ$ among the $n$ agents. Notably, our techniques naturally extend to general graphs, where leader election and spanning tree construction maintain the same round and memory complexities. Building on these foundations, agents count butterflies per node in $O(Δ)$ rounds and compute the total butterfly count of $G$ in $O(Δ+min{|A|,|B|})$ rounds.

Problem

• Develop agent-based algorithms for butterfly counting in bipartite graphs
• Achieve efficient leader election and spanning tree construction
• Extend techniques to general graphs with same complexity

Innovation

• Mobile agents count bipartite graph butterflies
• Leader election via novel meeting mechanism
• Efficient spanning tree construction algorithm