A link stream is a sequence of pairs of the form $(t,\{u,v\})$, where $t\in \mathbb{N}$ represents a time instant and $u\ne v$. Given an integer γ, the γ-edge between vertices u and v, starting at time t, is the set of temporally consecutive edges defined by $\{(t^{\prime },\{u,v\})|t^{\prime }\in 〚t,t+\gamma -1〛\}$. We introduce the notion of temporal matching of a link stream to be an independent γ-edge set belonging to the link stream. We show that the problem of computing a temporal matching of maximum size is NP-hard as soon as $\gamma >1$. We depict a kernelization algorithm parameterized by the solution size for the problem. As a byproduct we also give a 2-approximation algorithm.

Both our 2-approximation and kernelization algorithms are implemented and confronted to link streams collected from real world graph data. We observe that finding temporal matchings is a sensitive question when mining our data from such a perspective as: managing peer-working when any pair of peers X and Y are to collaborate over a period of one month, at an average rate of at least two email exchanges every week. We furthermore design a link stream generating process by mimicking the behavior of a random moving group of particles under natural simulation, and confront our algorithms to these generated instances of link streams. All the implementations are open source.

链接流是一系列形式的对 $（Ť，\{ü，v\}）$，在哪里 $Ť\in \mathbb{ñ}$ 代表一个瞬间 $ü\ne v$。给定一个整数γ，顶点u和v之间的γ边沿（从时间t开始）是由定义的时间上连续边沿的集合$\{（{Ť}^{\prime }，\{ü，v\}）|{Ť}^{\prime }\in 〚Ť，Ť+\gamma -\mathrm{1个}〛\}$。我们引入链接流的时间匹配的概念，使其成为属于链接流的独立γ边集。我们表明，计算最大大小的时间匹配的问题在NP上就很困难$\gamma >\mathrm{1个}$。我们描述了一种通过解决方案大小参数化的内核化算法。作为副产品，我们还给出了2近似算法。

我们的2逼近算法和内核化算法均已实现并面临着链接从现实世界图形数据收集的流的问题。我们观察到，从以下角度挖掘数据时，发现时间匹配是一个敏感的问题：当一对对等X和Y在一个月的时间内以至少两个平均比率进行协作时，管理对等工作每周进行电子邮件交流。我们还通过模拟自然模拟下的粒子的随机移动组的行为来设计链接流生成过程，并将我们的算法与链接流的这些生成实例相对。所有的实现都是开源的。