(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.

翻译：（超）图分解是一类旨在将大型（超）图拆解为更小子（超）图以简化分析的问题。其重要性在于能够对大规模复杂（超）图（如社交网络、化合物和计算机网络）实现高效计算。本论文探讨了多种（超）图分解问题，包括图划分、超图划分、局部图聚类、进程映射及符号图聚类，主要聚焦于流式算法、局部算法和多层算法。在流式算法方面，我们针对（超）图划分和进程映射提出了高效且效果显著的算法；在局部算法中，我们提出了基于给定模体分布的次线性算法，能够有效检测图中以指定种子节点为中心的高质量局部社区；在多层面，我们设计了面向进程映射和符号图聚类的高质量多层算法。本文详述了每种算法，并通过实验证明其相较于现有最优技术的优越性。结果表明，所提出算法在多种指标下均实现了更优性能与解质量，展现出显著的实践应用潜力。总体而言，本论文展示了先进组合算法技术在解决挑战性（超）图分解问题中的有效性。