Streaming, Local, and Multi-Level (Hyper)Graph Decomposition

TL;DR

This paper introduces advanced streaming, local, and multilevel algorithms for (hyper)graph decomposition, improving efficiency and solution quality for large complex graphs in various applications.

Contribution

It presents novel algorithms for (hyper)graph partitioning, process mapping, and community detection, with a focus on streaming, local, and multilevel approaches, demonstrating superior performance.

Findings

Algorithms outperform existing methods in efficiency

High-quality solutions achieved in various metrics

Effective in practical large-scale graph analysis

Abstract

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex (hyper)graphs, such as social networks, chemical compounds, and computer networks. This dissertation explores several types of (hyper)graph decomposition problems, including graph partitioning, hypergraph partitioning, local graph clustering, process mapping, and signed graph clustering. Our main focus is on streaming algorithms, local algorithms and multilevel algorithms. In terms of streaming algorithms, we make contributions with highly efficient and effective algorithms for (hyper)graph partitioning and process mapping. In terms of local algorithms, we propose sub-linear algorithms which are effective in detecting high-quality local communities around a given seed node in a graph based on the distribution of a given motif. In terms of multilevel algorithms, we engineer high-quality multilevel algorithms for process mapping and signed graph clustering. We provide a thorough discussion of each algorithm along with experimental results demonstrating their superiority over existing state-of-the-art techniques. The results show that the proposed algorithms achieve improved performance and better solutions in various metrics, making them highly promising for practical applications. Overall, this dissertation showcases the effectiveness of advanced combinatorial algorithmic techniques in solving challenging (hyper)graph decomposition problems.