Advances in Graph Analysis and Algorithms

The field of graph analysis and algorithms is rapidly advancing, with a focus on developing efficient and effective methods for processing and analyzing large-scale graphs. Recent developments have centered around improving the performance and scalability of graph algorithms, particularly in the context of streaming data and dynamic graphs. Notably, researchers have made significant progress in designing algorithms for constructing long paths in graph streams, spectral partitioning of directed graphs, and quality control in sublinear time. These innovations have far-reaching implications for various applications, including network analysis, recommendation systems, and social network analysis. Noteworthy papers in this area include the work on constructing long paths in graph streams, which presents algorithms and space lower bounds for both undirected and directed graphs. Another notable paper presents a new approach to spectral partitioning of directed graphs, which outperforms the state-of-the-art Gorder algorithm by up to 17 times. The paper on quality control in sublinear time introduces a new class of algorithmic problems and presents efficient algorithms for solving these problems in the context of random graphs.

Sources

Constructing Long Paths in Graph Streams

Symmetry-breaking symmetry in directed spectral partitioning

Quality control in sublinear time: a case study via random graphs

Dense Subgraph Clustering and a New Cluster Ensemble Method

Polynomial Property Testing

Effective Clustering for Large Multi-Relational Graphs

Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders

Accelerating Historical K-Core Search in Temporal Graphs

Spectral Refutations of Semirandom $k$-LIN over Larger Fields

Optimal $(\alpha,\beta)$-Dense Subgraph Search in Bipartite Graphs

Hypergraph Splitting-Off via Element-Connectivity Preserving Reductions

DTC: Real-Time and Accurate Distributed Triangle Counting in Fully Dynamic Graph Streams

Distributed Sparsest Cut via Eigenvalue Estimation

Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective

Reducing Shortcut and Hopset Constructions to Shallow Graphs

Directed and Undirected Vertex Connectivity Problems are Equivalent for Dense Graphs

Sharp Online Hardness for Large Balanced Independent Sets

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