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(Hyper)Graph decomposition is a family of problems that aim to break downlarge (hyper)graphs into smaller sub(hyper)graphs for easier analysis. Theimportance of this lies in its ability to enable efficient computation on largeand complex (hyper)graphs, such as social networks, chemical compounds, andcomputer networks. This dissertation explores several types of (hyper)graphdecomposition problems, including graph partitioning, hypergraph partitioning,local graph clustering, process mapping, and signed graph clustering. Our mainfocus is on streaming algorithms, local algorithms and multilevel algorithms.In terms of streaming algorithms, we make contributions with highly efficientand effective algorithms for (hyper)graph partitioning and process mapping. Interms of local algorithms, we propose sub-linear algorithms which are effectivein detecting high-quality local communities around a given seed node in a graphbased on the distribution of a given motif. In terms of multilevel algorithms,we engineer high-quality multilevel algorithms for process mapping and signedgraph clustering. We provide a thorough discussion of each algorithm along withexperimental results demonstrating their superiority over existingstate-of-the-art techniques. The results show that the proposed algorithmsachieve improved performance and better solutions in various metrics, makingthem highly promising for practical applications. Overall, this dissertationshowcases the effectiveness of advanced combinatorial algorithmic techniques insolving challenging (hyper)graph decomposition problems.

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