Motivo: fast motif counting via succinct color coding and adaptive sampling
Marco Bressan, Stefano Leucci, Alessandro Panconesi

TL;DR
Motivo is a scalable, accurate motif counting algorithm for large graphs that leverages novel data structures, biased coloring, and adaptive sampling to efficiently count complex motifs on massive networks.
Contribution
The paper introduces Motivo, a new motif counting algorithm that significantly improves scalability and accuracy through innovative data structures, biased coloring, and adaptive sampling strategies.
Findings
Counts 7-node motifs on graphs with 65M nodes and 1.8B edges in 40 minutes
Accurately counts ~10,000 8-node motifs where previous algorithms fail
Operates efficiently on a high-end desktop machine
Abstract
The randomized technique of color coding is behind state-of-the-art algorithms for estimating graph motif counts. Those algorithms, however, are not yet capable of scaling well to very large graphs with billions of edges. In this paper we develop novel tools for the `motif counting via color coding' framework. As a result, our new algorithm, Motivo, is able to scale well to larger graphs while at the same time provide more accurate graphlet counts than ever before. This is achieved thanks to two types of improvements. First, we design new succinct data structures that support fast common color coding operations, and a biased coloring trick that trades accuracy versus running time and memory usage. These adaptations drastically reduce the time and memory requirements of color coding. Second, we develop an adaptive graphlet sampling strategy, based on a fractional set cover problem, that…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Theory and Algorithms · Complexity and Algorithms in Graphs
