We consider the task of estimating a network cascade as fast as possible. The cascade is assumed to spread according to a general Susceptible-Infected process with heterogeneous transmission rates from an unknown source in the network. While the propagation is not directly observable, noisy information about its spread can be gathered through multiple rounds of error-prone diagnostic testing. We propose a novel adaptive procedure which quickly outputs an estimate for the cascade source and the full spread under this observation model. Remarkably, under mild conditions on the network topology, our procedure is able to estimate the full spread of the cascade in an $n$-vertex network, before $\mathrm{poly log}(n)$ vertices are affected by the cascade. We complement our theoretical analysis with simulation results illustrating the effectiveness of our methods.

翻译：我们考虑尽可能快地估计网络级联的任务。假设级联根据一般的易感-感染过程传播，该过程具有从网络中未知源头出发的异质传播速率。虽然传播过程无法直接观测，但可以通过多轮易出错的诊断测试收集关于其扩散的含噪信息。我们提出了一种新颖的自适应方法，在这种观测模型下能够快速输出级联源头及完整传播范围的估计。值得注意的是，在网络拓扑的温和条件下，我们的方法能够在级联影响到$n$顶点网络中的$\mathrm{poly log}(n)$个顶点之前，估计出该级联的完整传播范围。我们通过仿真结果补充理论分析，展示了所提方法的有效性。