在线社交网络中阈值激活问题的可扩展双准则算法
Scalable Bicriteria Algorithms for the Threshold Activation Problem in Online Social Networks
摘要：
我们考虑阈值激活问题（TAP）：给定社交网络$G$和正阈值$T$，找到一个最小大小的种子集$A$，可以触发至少$T$的预期激活。我们介绍了第一个可扩展的，可并行化的算法，其性能保证适用于具有数百万节点和边缘的数据集;我们利用TAP解决方案的双标准性质，允许用户通过参数$α\in (0,1)$控制算法的运行时间与准确性：给定$η> 0$，我们的算法以概率$1 - η$返回具有大于$T - 2 αT$的预期激活的解$A$，并且解$A$的大小在最佳大小的因子$1 + 4 αT + \log ( T )$内。该算法在时间上运行$O \left( α^{-2}\log \left( n / η\right) (n + m) |A| \right)$，其中$n$、$m$是指网络中的节点、边的数量。性能保证适用于内部影响的一般触发模型，也包括外部影响，只要满足一定的条件，种子选择的成本效益。
英文摘要：
We consider the Threshold Activation Problem (TAP): given social network $G$ and positive threshold $T$, find a minimum-size seed set $A$ that can trigger expected activation of at least $T$. We introduce the first scalable, parallelizable algorithm with performance guarantee for TAP suitable for datasets with millions of nodes and edges; we exploit the bicriteria nature of solutions to TAP to allow the user to control the running time versus accuracy of our algorithm through a parameter $α\in (0,1)$: given $η> 0$, with probability $1 - η$ our algorithm returns a solution $A$ with expected activation greater than $T - 2 αT$, and the size of the solution $A$ is within factor $1 + 4 αT + \log ( T )$ of the optimal size. The algorithm runs in time $O \left( α^{-2}\log \left( n / η\right) (n + m) |A| \right)$, where $n$, $m$, refer to the number of nodes, edges in the network. The performance guarantee holds for the general triggering model of internal influence and also incorporates external influence, provided a certain condition is met on the cost-effectivity of seed selection.
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