发表机构
School of Data Science, Fudan University（复旦大学数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出确定性加速局部PageRank算法，在无图级预处理下达到多对数开销，并给出随机算法及复杂度界限。
AI 中文摘要
局部PageRank算法寻求稀疏近似，其工作量与图大小无关。我们给出一个确定性算法，用于正则化个性化PageRank，在加性目标精度$\epsilon$下，局部工作量为$\widetilde{\mathcal{O}}(1/(\rho\sqrt\alpha))$，其中$\alpha$是惰性传送参数，$\rho$是正则化参数。精度仅以多对数方式进入。该界限涵盖发现、重复邻域扫描、数值更新、认证和输出，无需图级预处理或提供的解支持。该算法将正则化延续与受度缩放盒和质量上限约束的加速校正相结合。同一递推的两个能量控制目标收敛和激活坐标的响应。一个选定流论证限制了累计扫描体积，一个稀疏阈值报告器实现了该界限。我们还为有理输入指定了一个有界算术实现。第二个随机算法使用支持安全的阈值批次。一个块Cholesky和Chebyshev论证限制了它们的深度，认证的SDD求解给出期望工作量$\widetilde{\mathcal{O}}(V_*\min\{k_*,\alpha^{-1/2}\})$，其中$k_*$和$V_*$是最优支持的基数和度体积。两种方法都意味着相应的加速度归一化PPR近似。Cui、Wei和Yang于2026年9月同时发布的预印本也达到了随机工作量规模。我们的主要区别是确定性局部加速，仅有多对数开销且无SDD预言机。
英文摘要
Local PageRank algorithms seek sparse approximations with work independent of graph size. We give a deterministic algorithm for regularized personalized PageRank with additive objective accuracy $ε$ in $\widetilde{\mathcal{O}}(1/(ρ\sqrtα))$ local work, where $α$ is the lazy teleportation parameter and $ρ$ is the regularizer. Accuracy enters only polylogarithmically. The bound charges discovery, repeated neighborhood scans, numerical updates, certification, and output, without graph-wide preprocessing or a supplied solution support. The algorithm combines regularization continuation with accelerated corrections constrained by a degree-scaled box and a mass cap. Two energies for the same recurrence control objective convergence and the response that activates coordinates. A selected-flow argument bounds cumulative scanned volume, and a sparse threshold reporter realizes the bound. We also specify a bounded-arithmetic implementation for rational inputs. A second, randomized algorithm uses support-safe threshold batches. A block-Cholesky and Chebyshev argument bounds their depth, and certified SDD solves give expected work $\widetilde{\mathcal{O}}(V_*\min\{k_*,α^{-1/2}\})$, where $k_*$ and $V_*$ are the optimal support's cardinality and degree volume. Both methods imply the corresponding accelerated degree-normalized PPR approximation. The concurrent September 2026 preprint of Cui, Wei, and Yang also attains the randomized work scale. Our principal distinction is deterministic local acceleration with only polylogarithmic overhead and no SDD oracle.
