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版本更新 · v2arXiv:2610.06959

Nearly optimal Personalized PageRank computation

Rong-Hua Li, Quanqing Xu, Yichun Yang, Junjie Zhou

原文摘要

We study the fundamental problem of computing Personalized PageRank (PPR) on an undirected and unweighted graph $G$. We focus on the $\eps$-error guarantee introduced by Andersen, Chung, and Lang [ACL; FOCS 2006 $\&$ Internet Math 2007]. Their classic local push method computes an approximate PPR vector satisfying the ACL $\eps$-error guarantee in $O((α\eps)^{-1})$ time, where $α$ is the teleportation parameter. This problem has a lower bound $Ω(\eps^{-1})$. Working with idealized SDDM solves, we eliminate the dependence on $α$ and present an algorithm that achieves the same error guarantee in $O(\eps^{-1-o(1)})$ time. Consequently, we obtain a nearly optimal algorithm for PPR computation under the ACL error guarantee, and a nearly linear algorithm for local graph clustering with complexity independent of $φ$.

cs.DS · cs.CC

版本更新 · v2arXiv:2604.07794

Density Decomposition on Hypergraphs

Xiaoyu Leng, Hongchao Qin, Rong-Hua Li, Guoren Wang

原文摘要

Hypergraphs capture higher-order interactions involving multiple entities. Existing decomposition models, such as $k$-core and nbr-$k$-core, rely on degree or neighborhood constraints and may overlook fine-grained density variations. We propose a $(k,δ)$-dense subhypergraph model based on capped hyperedge contributions. For each parameter pair, the unique dense set is the inclusionwise smallest maximizer of a penalized capped hyperedge contribution. These dense sets form a nested hierarchy characterized by egalitarian $δ$-orientations and hypergraph reachability. We develop three algorithms for dense subhypergraph search and two for complete density decomposition. Both decomposition algorithms use integral flow balancing: Flow-Decomp extracts density levels through strongly connected component condensation, while Reverse-Decomp uses direct reverse propagation. Once an egalitarian orientation is obtained, both recover all density levels in linear time. We further derive sandwich bounds that restrict computation to equivalent residual subproblems and develop incremental algorithms for maintaining the hierarchy under hyperedge insertions and deletions. Experiments on nine real-world hypergraphs, including datasets with over 15 million vertices, compare our methods with four established decomposition models. The results show that Reverse-Decomp improves decomposition efficiency, incremental maintenance outperforms recomputation in the tested settings, and the proposed model captures density structures overlooked by degree-based decompositions.

cs.SI · cs.DS

新论文 · v1arXiv:2610.36444

RouteDRAG: Learning to Route and Control Agentic Execution for Multimodal Document RAG

Zekai Chen, Hao Zhu, Yu Liu, Xunkai Li, Zejian Kang, Rui Qian, Quanjiang Li, Rong-Hua Li

原文摘要

Web-based applications increasingly rely on understanding long multimodal documents, where answering questions often requires combining information across pages, tables, and figures. Agentic retrieval-augmented generation addresses these tasks through iterative retrieval and reasoning. However, Agentic execution is not always necessary, introducing additional computation and potentially incorrect answers. Our empirical analysis reveals that Agentic execution provides query-dependent benefits, while additional operations may improve, preserve, or degrade answer accuracy. These findings motivate controlling both Agent invocation and subsequent execution. To address these challenges, we propose RouteDRAG, a learning-based framework comprising four components. Unified Document Index organizes multimodal content into a graph-backed index and derives query representations from initial retrieval. Adaptive Path Routing preserves exact answering and predicts the relative benefit of Agent over shorter execution paths. Dynamic Agent Execution maintains an evolving workspace and refines Planner proposals to control tool use and termination. Sequential Policy Learning first trains operation control from observed outcomes and then trains path routing using the resulting Agent's performance. Across two benchmarks, RouteDRAG achieves an average accuracy improvement of 3.47 percentage points over shorter-path-only execution while assigning only 79.3% of queries to Agent. Notably, it also surpasses uniform Agent execution on both benchmarks while requiring fewer answering calls. Our code is now available at https://github.com/Ereshkigal1/RouteDRAG.

cs.AI