Influence maximization (IM) is a widely studied problem in social networks, which aims at finding a seed set with limited size that can maximize the expected number of influenced users. However, existing studies haven't considered the matching relationship, which refers to such scenarios that influenced users seek matched partners among the influenced users, such as time matching with friends to watch movie, or matching for opposite sex in the blind date. In this paper, we investigate different matching scenarios and propose online-matching (offline-matching), in which the matching and influence propagation are simultaneous (asynchronous). For the matching result, we introduce two matched types ‘s-$matched$’, i.e., $i\to j$ and ‘d-$matched$’, i.e., $i\leftrightarrow j$. Then, we formulate the matching influence maximization (MM) problem to optimize a limited seed set that maximizes the expected number of matched users. We prove that the MM problem is NP-hard and the computation of the matching influence is #P-hard. Next, we analyze the submodularity of the matching influence. To address the problem, we propose efficient methods OPMM (SAMM) to solve the MM in online-matching (offline-matching) with $(1-1/e-ϵ)$-approximation ($\beta (1-1/e-ϵ)$-approximation) guarantee. Experiments on the real-world datasets show our algorithms outperform state of the art algorithms in terms of more accurate matching propagation results.

影响力最大化（IM）是社交网络中广泛研究的问题，其目的是找到具有有限大小的种子集，该种子集可以最大化受影响用户的预期数量。但是，现有研究尚未考虑匹配关系，而是指受影响用户在受影响用户中寻找匹配伙伴的情况，例如与朋友看电影的时间匹配或相亲中的异性匹配。在本文中，我们研究了不同的匹配方案，并提出了在线匹配（offline-matching），其中匹配和影响传播是同时的（异步的）。对于匹配结果，我们引入两个匹配的类型'小号-$米\mathrm{一种}ŤCHËd$'，即 $\mathrm{一世}\to Ĵ$和“ d -$米\mathrm{一种}ŤCHËd$'，即 $\mathrm{一世}\leftrightarrow Ĵ$。然后，我们制定匹配影响最大化（MM）问题，以优化使期望的匹配用户数量最大化的有限种子集。我们证明MM问题是NP难的，匹配影响的计算是#P难的。接下来，我们分析匹配影响的次模量。为了解决该问题，我们提出了有效的方法OPMM（SAMM）来解决MM的在线匹配（离线匹配）问题，$（\mathrm{1个}-\mathrm{1个}/Ë-ϵ）$-近似（$\beta （\mathrm{1个}-\mathrm{1个}/Ë-ϵ）$-近似）保证。在真实数据集上进行的实验表明，就更准确的匹配传播结果而言，我们的算法优于最新算法。