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- W2904272488 abstract "A link stream is a sequence of pairs of the form $(t,{u,v})$, where $tinmathbb N$ represents a time instant and $uneq v$. Given an integer $gamma$, the $gamma$-edge between vertices $u$ and $v$, starting at time $t$, is the set of temporally consecutive edges defined by ${(t',{u,v}) | t' in [t,t+gamma-1]}$. We introduce the notion of temporal matching of a link stream to be an independent $gamma$-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 behaviour 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." @default.
- W2904272488 created "2018-12-22" @default.
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- W2904272488 date "2018-12-20" @default.
- W2904272488 modified "2023-09-25" @default.
- W2904272488 title "Temporal Matching" @default.
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