Advances in Graph Coarsening and Optimization

The field of graph theory and optimization is rapidly advancing, with a focus on improving the efficiency and accuracy of various algorithms and techniques. One of the key areas of research is graph coarsening, which aims to reduce the size of a graph while preserving its essential properties. Recent work has introduced new notions of reduction matrices and lifting matrices, allowing for more flexible and effective coarsening methods. Additionally, researchers have made significant progress in solving long-standing problems, such as the Global Minimum Vertex-Cut problem, with new algorithms achieving better time complexities. Furthermore, there have been advancements in graph domain adaptation, spectral partitioning, and encoding techniques for graph problems, which have the potential to impact a wide range of applications. Noteworthy papers include one that breaks the 28-year-old bound for the general weighted Global Minimum Vertex-Cut problem, and another that proposes a novel multi-source graph domain adaptation approach for social bot detection. Overall, these developments are paving the way for more efficient and effective solutions to complex graph-related problems.

Sources

Taxonomy of reduction matrices for Graph Coarsening

Breaking the O(mn)-Time Barrier for Vertex-Weighted Global Minimum Cut

BotTrans: A Multi-Source Graph Domain Adaptation Approach for Social Bot Detection

Spectral partitioning of graphs into compact, connected regions

Asymptotically Smaller Encodings for Graph Problems and Scheduling

The Complexity of Counting Small Sub-Hypergraphs

Simpler, Better, Faster, Stronger: Revisiting a Successful Reduction Rule for Dominating Set

Efficient space reduction techniques by optimized majority rules for the Kemeny aggregation problem

Learn to Vaccinate: Combining Structure Learning and Effective Vaccination for Epidemic and Outbreak Control

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