社交网络中有时延限制的目标集选择
Latency-Bounded Target Set Selection in Social Networks
摘要：
出于社会学，经济学和医学中的应用，我们研究的目标集选择问题，首先提出了肯普，克莱因伯格和塔尔多斯的变种。在我们的场景中，给定一个图$G=(V,E)$，每个顶点$v$（\emph{thresholds}）的整数值$t(v)$，目标是确定一个小的顶点集（\emph{target set}），该顶点集将给定数量（或给定子集）的$G$ \emph{within}的顶点激活规定数量的轮。$G$中的激活过程如下进行：最初，在第0轮，目标集中的所有顶点都被激活;随后，在每一轮$r\geq 1$，如果$t(v)$的至少$t(v)$的邻居在第$r-1$轮之前已经是活动的，则$G$的每个顶点都被激活。已知的是，找到最终激活整个图$G$的最小基数目标集的问题很难近似为比$O(2^{\log^{1-ε}|V|})$更好的因子。本文给出了求有界树宽图的最小基数目标集的\emph{exact}多项式时间算法和树的\emph{exact}线性时间算法。
英文摘要：
Motivated by applications in sociology, economy and medicine, we study variants of the Target Set Selection problem, first proposed by Kempe, Kleinberg and Tardos. In our scenario one is given a graph $G=(V,E)$, integer values $t(v)$ for each vertex $v$ (\emph{thresholds}), and the objective is to determine a small set of vertices (\emph{target set}) that activates a given number (or a given subset) of vertices of $G$ \emph{within} a prescribed number of rounds. The activation process in $G$ proceeds as follows: initially, at round 0, all vertices in the target set are activated; subsequently at each round $r\geq 1$ every vertex of $G$ becomes activated if at least $t(v)$ of its neighbors are already active by round $r-1$. It is known that the problem of finding a minimum cardinality Target Set that eventually activates the whole graph $G$ is hard to approximate to a factor better than $O(2^{\log^{1-ε}|V|})$. In this paper we give \emph{exact} polynomial time algorithms to find minimum cardinality Target Sets in graphs of bounded clique-width, and \emph{exact} linear time algorithms for trees.
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