AOT: Pushing the Efficiency Boundary of Main-memory Triangle Listing

TL;DR

This paper introduces AOT, an adaptive orientation-based algorithm that significantly improves the efficiency of in-memory triangle listing, especially for large-scale graphs, by combining theoretical optimality with practical performance enhancements.

Contribution

It proposes an adaptive orientation technique and the AOT algorithm, achieving the best theoretical and practical performance for in-memory triangle listing.

Findings

AOT outperforms state-of-the-art algorithms on large real-world graphs.

Theoretical time complexity is proven to be optimal among in-memory methods.

Experimental results show superior efficiency on graphs with billions of edges.

Abstract

Triangle listing is an important topic significant in many practical applications. Efficient algorithms exist for the task of triangle listing. Recent algorithms leverage an orientation framework, which can be thought of as mapping an undirected graph to a directed acylic graph, namely oriented graph, with respect to any global vertex order. In this paper, we propose an adaptive orientation technique that satisfies the orientation technique but refines it by traversing carefully based on the out-degree of the vertices in the oriented graph during the computation of triangles. Based on this adaptive orientation technique, we design a new algorithm, namely aot, to enhance the edge-iterator listing paradigm. We also make improvements to the performance of aot by exploiting the local order within the adjacent list of the vertices. We show that aot is the first work which can achieve best performance in terms of both practical performance and theoretical time complexity. Our comprehensive experiments over $16$ real-life large graphs show a superior performance of our \aot algorithm when compared against the state-of-the-art, especially for massive graphs with billions of edges. Theoretically, we show that our proposed algorithm has a time complexity of $\Theta(\sum_{ \langle u,v \rangle \in \vec{E} } \min\{ deg^{+}(u),deg^{+}(v)\}))$, where $\vec{E}$ and $deg^{+}(x)$ denote the set of directed edges in an oriented graph and the out-degree of vertex $x$ respectively. As to our best knowledge, this is the best time complexity among in-memory triangle listing algorithms.