在多项式时间内由稠密三元组构建k级系统发育网络
Level-k Phylogenetic Network can be Constructed from a Dense Triplet Set in Polynomial Time
摘要：
给定一个稠密的三元组集合$\mathcal{T}$，会产生两个有趣的问题：是否存在与$\mathcal{T}$一致的系统发育网络？如果是这样，我们能找到一个有效的算法来构建一个吗？对于等级为$k=0$或1或2的网络的情况，这些问题用有效的多项式算法来回答。对于更高级别的$k$，部分答案最近获得了简单网络的$O(|\mathcal{T}|^{k+1})$时间算法。在本文中，我们给出了一个完整的答案一般情况。其主要思想是在k级网络中使用SN-集的一个特殊性质。因此，我们也可以在多项式时间内找到具有最小网格数的k级网络。
英文摘要：
Given a dense triplet set $\mathcal{T}$, there arise two interesting questions: Does there exists any phylogenetic network consistent with $\mathcal{T}$? And if so, can we find an effective algorithm to construct one? For cases of networks of levels $k=0$ or 1 or 2, these questions were answered with effective polynomial algorithms. For higher levels $k$, partial answers were recently obtained with an $O(|\mathcal{T}|^{k+1})$ time algorithm for simple networks. In this paper we give a complete answer to the general case. The main idea is to use a special property of SN-sets in a level-k network. As a consequence, we can also find the level-k network with the minimum number of reticulations in polynomial time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
