Streaming and Batch Algorithms for Truss Decomposition

TL;DR

This paper introduces a theoretical framework and efficient algorithms for incrementally updating truss decompositions in large dynamic graphs, significantly improving update speed and handling batch modifications effectively.

Contribution

It provides a new theory for how truss decompositions change with edge additions and develops optimized incremental and batch algorithms for dynamic graph analysis.

Findings

Over 250,000x speedup in edge insertion updates on large graphs

Batch update algorithm outperforms incremental updates in efficiency

Algorithms tested on real-world datasets with significant performance gains

Abstract

Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be updated as well. This work focuses on the problem of incrementally updating an existing truss decomposition and makes the following three significant contributions. First, it presents a theory that identifies how the truss decomposition can change as new edges get added. Second, it develops an efficient incremental algorithm that incorporates various optimizations to update the truss decomposition after every edge addition. These optimizations are designed to reduce the number of edges that are explored by the algorithm. Third, it extends this algorithm to batch updates (i.e., where the truss decomposition needs to be updated after a set of edges are added), which reduces the overall computations that need to be performed. We evaluated the performance of our algorithms on real-world datasets. Our incremental algorithm achieves over 250000x average speedup for inserting an edge in a graph with 10 million edges relative to the non-incremental algorithm. Further, our experiments on batch updates show that our batch algorithm consistently performs better than the incremental algorithm.