有向无环图中的多叶生成树形图
Leafy Spanning Arborescences in DAGs
AI总结：
针对有根有向无环图上最大叶子生成树形图这一MaxSNP难问题，本文将已有2-近似算法改进为(3/2)-近似，并推导了其顶点加权版本的不可近似性结果。
摘要：
计算机网络中的广播是一种将消息同时传输给所有接收方的方法。在这种场景下，通常使用具有大量叶子的树来执行广播，因为内部节点必须转发接收到的消息，而叶子节点仅作为接收端。我们研究如下基础问题：给定有向图$D$，若存在生成树形图，找出其中叶子数最多的一棵。本文聚焦于有根有向无环图这一类别，已知该问题在此类图上属于MaxSNP难问题。此前针对这类有向图上的该问题，已有一个2-近似算法。我们改进了这一结果，提出了一个(3/2)-近似算法。我们还改编了无向情形下的一个结果，推导出有根有向无环图上最大叶子生成树形图的顶点加权版本的一个不可近似性结果。
英文摘要：
Broadcasting in a computer network is a method of transferring a message to all recipients simultaneously. It is common in this situation to use a tree with many leaves to perform the broadcast, as internal nodes have to forward the messages received, while leaves are only receptors. We consider the subjacent problem of, given a directed graph~$D$, finding a spanning arborescence of D, if one exists, with the maximum number of leaves. In this paper, we concentrate on the class of rooted directed acyclic graphs, for which the problem is known to be MaxSNP-hard. A 2-approximation was previously known for this problem on this class of directed graphs. We improve on this result, presenting a (3/2)-approximation. We also adapt a result for the undirected case and derive an inapproximability result for the vertex-weighted version of Maximum Leaf Spanning Arborescence on rooted directed acyclic graphs.
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