AI 中文总结
研究提出一种无求解器并行谱稀疏化算法，依赖并行低直径分解和独立采样，改进了此前方法，消除对目标近似精度ε的依赖，通过估计边的鲁棒连通性进行子采样，并经实验验证性能良好。
AI 中文摘要
我们提出了一种新的无求解器并行谱稀疏化算法，用于加权图，该算法仅依赖并行低直径分解和独立采样。这是自2014年Koutis以来对先前无求解器并行稀疏化方法的首次算法改进，并且对于一种实用算法而言，首次消除了算法工作和深度对目标近似精度ε的任何依赖。我们的算法根据Kapralov和Panigrahy（2012）引入的边的鲁棒连通性对边进行子采样。我们展示了如何以一种极其简单的方式估计G的鲁棒连通性：创建多个随机子图G_p，其中G中的每条边以概率p_e = min{w_e·p, 1}独立子采样。然后，在每个图中运行低直径分解。如果u和v在LDD中经常共享一个簇，那么这为边e = (u, v)的鲁棒连通性提供了一个上界。对概率p的O(log n)个不同值仔细调用此过程，然后使我们能够获得足够好的子采样估计。我们还通过实验评估对理论进行补充，证明了在相关图和稀疏度范围内的强大性能。
英文摘要
We present a new solver-free parallel spectral sparsification algorithm for weighted graphs that relies only on parallel low-diameter decompositions and independent sampling. This yields the first algorithmic improvement over prior, solver-free parallel sparsification approaches since Koutis (2014) and, for the first time for a practical algorithm, eliminates any dependence on the target approximation accuracy $ε$ in the algorithm's work and depth. Our algorithm works by sub-sampling edges according to their robust connectivity, as introduced by Kapralov and Panigrahy (2012). We show how to estimate the robust connectivities of $G$ in an extremely simple manner: we create multiple random sub graphs $G_p$, where each edge in $G$ is sub-sampled independently with probability $p_e = \min \{w_e \cdot p, 1\}$. Then, we run a Low Diameter Decomposition in each of the graphs. If $u$ and $v$ often share a cluster in the LDDs, then this provides us with an upper bound on the robust connectivity of the edge $e = (u,v)$. Carefully invoking this procedure for $O(\log n)$ different values of the probabilities $p$ then allows us to obtain sufficiently good estimates for sub-sampling. We additionally complement the theory with an experimental evaluation demonstrating strong performance across relevant graphs and sparsity regimes.
CommentsSPAA 2026
